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	<id>https://wikisofia.cz/w/index.php?action=history&amp;feed=atom&amp;title=Filtr</id>
	<title>Filtr - Historie editací</title>
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	<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Filtr&amp;action=history"/>
	<updated>2026-04-19T23:11:03Z</updated>
	<subtitle>Historie editací této stránky</subtitle>
	<generator>MediaWiki 1.33.0</generator>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8203&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: /* Zdroje */</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8203&amp;oldid=prev"/>
		<updated>2014-11-13T17:02:45Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Zdroje&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 13. 11. 2014, 17:02&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l21&quot; &gt;Řádek 21:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 21:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Zdroje ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Zdroje ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;Poznámky z přednášek Booleovy algebry na [http://logika.ff.cuni.cz/ Katedře Logiky].[[Kategorie:Struktury a algebry]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Poznámky z přednášek Booleovy algebry na [http://logika.ff.cuni.cz/ Katedře Logiky].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Kategorie:Struktury a algebry]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8202&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova v 13. 11. 2014, 17:02</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8202&amp;oldid=prev"/>
		<updated>2014-11-13T17:02:16Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 13. 11. 2014, 17:02&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot; &gt;Řádek 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Duál k filtru je '''[[Ideál|ideál]]''': &amp;lt;math&amp;gt;F^{*} = \{X\smallsetminus A: A \in F\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Duál k filtru je '''[[Ideál|ideál]]''': &amp;lt;math&amp;gt;F^{*} = \{X\smallsetminus A: A \in F\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;math&amp;gt;F_{n}&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;$ &lt;/del&gt;je '''triviální filtr''', pokud &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;$&lt;/del&gt;F_{n} = \{X \subseteq \mathbb{N}: n \in F_{n}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;math&amp;gt;F_{n}&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;je '''triviální filtr''', pokud &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;F_{n} = \{X \subseteq \mathbb{N}: n \in F_{n}\}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt;, pak platí:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt;, pak platí:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8201&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova v 13. 11. 2014, 17:01</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8201&amp;oldid=prev"/>
		<updated>2014-11-13T17:01:25Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 13. 11. 2014, 17:01&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l13&quot; &gt;Řádek 13:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 13:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# A je '''maximální filtr''', pokud &amp;lt;math&amp;gt;\forall C \supset A&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; není filtr&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# A je '''maximální filtr''', pokud &amp;lt;math&amp;gt;\forall C \supset A&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; není filtr&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Výše uvedené tři podmínky jsou ekvivalentní.&amp;lt;br /&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Výše uvedené tři podmínky jsou ekvivalentní.&amp;lt;br /&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Důkaz:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Důkaz:&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=&amp;quot;Honzík&amp;quot;&amp;gt;Honzík Radek. Boolean algebras (Lecture notes). (2012).&amp;lt;/ref&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:# Je-li U ultrafiltr, pak je prvofiltr.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:# Je-li U ultrafiltr, pak je prvofiltr.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:# Je-li U prvofiltr, pak je maximální.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:# Je-li U prvofiltr, pak je maximální.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l19&quot; &gt;Řádek 19:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 19:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt; filtr, pak &amp;lt;math&amp;gt;\exists U \supseteq F&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; je ultrafiltr.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt; filtr, pak &amp;lt;math&amp;gt;\exists U \supseteq F&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; je ultrafiltr.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Zdroje ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;references/&amp;gt;Poznámky z přednášek Booleovy algebry na [http://logika.ff.cuni.cz/ Katedře Logiky].[[Kategorie:Struktury a algebry]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8200&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: Založena nová stránka s textem „Množina &lt;math&gt;F \subseteq \mathcal{P}(X)&lt;/math&gt; je filtr, pokud platí: # &lt;math&gt;\emptyset \notin F, X \in F&lt;/math&gt; # &lt;math&gt;A, B \in F \rightarrow A \wedge…“</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Filtr&amp;diff=8200&amp;oldid=prev"/>
		<updated>2014-11-13T16:46:18Z</updated>

		<summary type="html">&lt;p&gt;Založena nová stránka s textem „Množina &amp;lt;math&amp;gt;F \subseteq \mathcal{P}(X)&amp;lt;/math&amp;gt; je filtr, pokud platí: # &amp;lt;math&amp;gt;\emptyset \notin F, X \in F&amp;lt;/math&amp;gt; # &amp;lt;math&amp;gt;A, B \in F \rightarrow A \wedge…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Nová stránka&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Množina &amp;lt;math&amp;gt;F \subseteq \mathcal{P}(X)&amp;lt;/math&amp;gt; je filtr, pokud platí:&lt;br /&gt;
# &amp;lt;math&amp;gt;\emptyset \notin F, X \in F&amp;lt;/math&amp;gt;&lt;br /&gt;
# &amp;lt;math&amp;gt;A, B \in F \rightarrow A \wedge B \in F&amp;lt;/math&amp;gt;&lt;br /&gt;
# &amp;lt;math&amp;gt;A \subseteq B, A \in F \rightarrow B \in F&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Duál k filtru je '''[[Ideál|ideál]]''': &amp;lt;math&amp;gt;F^{*} = \{X\smallsetminus A: A \in F\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;F_{n}$ je '''triviální filtr''', pokud $F_{n} = \{X \subseteq \mathbb{N}: n \in F_{n}\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt;, pak platí:&lt;br /&gt;
# A je '''ultrafiltr''', pokud &amp;lt;math&amp;gt;(\forall a \in B)(a \in A \vee -a \in A)&amp;lt;/math&amp;gt;&lt;br /&gt;
# A je '''prvofiltr''' ''(primefilter)'', pokud &amp;lt;math&amp;gt;(a \vee b \in A \rightarrow (a \in A \vee b \in A)&amp;lt;/math&amp;gt;&lt;br /&gt;
# A je '''maximální filtr''', pokud &amp;lt;math&amp;gt;\forall C \supset A&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; není filtr&lt;br /&gt;
Výše uvedené tři podmínky jsou ekvivalentní.&amp;lt;br /&amp;gt;&lt;br /&gt;
Důkaz:&lt;br /&gt;
:# Je-li U ultrafiltr, pak je prvofiltr.&lt;br /&gt;
:# Je-li U prvofiltr, pak je maximální.&lt;br /&gt;
:# Je-li U maximální, pak je ultra.&lt;br /&gt;
&lt;br /&gt;
Je-li &amp;lt;math&amp;gt;A \subseteq \mathbb{B}^{+}&amp;lt;/math&amp;gt; filtr, pak &amp;lt;math&amp;gt;\exists U \supseteq F&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; je ultrafiltr.&lt;/div&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
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