http://www.multimediaexpo.cz/mmecz/index.php?action=history&feed=atom&title=Podsvaz 2026-07-03T01:36:31Z Historie editací této stránky MediaWiki 1.16.5 http://www.multimediaexpo.cz/mmecz/index.php?title=Podsvaz&diff=2846000&oldid=prev 2024-04-14T12:21:07Z

<p>+ Aktualizace</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Starší verze</td> <td colspan='2' style="background-color: white; color:black;">Verze z 14. 4. 2024, 12:21</td> </tr><tr><td colspan="2" class="diff-lineno">Řádka 1:</td> <td colspan="2" class="diff-lineno">Řádka 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">{{Wikipedia-cs|</del>Podsvaz|<del class="diffchange diffchange-inline">700}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''</ins>Podsvaz<ins class="diffchange diffchange-inline">''' je [[podmnožina]] [[Svaz (matematika)</ins>|<ins class="diffchange diffchange-inline">svazu]], která je sama také svazem.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Definice ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Nechť (A,∧,∨) je svaz a B je neprázdná podmnožina A. Pak B se nazývá podsvazem svazu A, platí-li, že B je uzavřená vzhledem ke svazovým&nbsp; operacím „∧“ a „∨“. tedy</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;big&gt;\(\forall a,b \in B : a \wedge b \in B , a \vee b \in B\)&lt;/big&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Příklad ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{RIGHTTOC}}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Množina B = {1,2,3,5,6,10,15,30} všech přirozených [[Dělitel (dělení)|dělitelů]] čísla 30 je podsvazem svazu &lt;big&gt;\((\mathbb{N},|)\)&lt;/big&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Vlastnosti ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Jestliže B je podsvaz svazu A, pak B je svazem vzhledem k indukovanému uspořádání.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Obráceně to nemusí platit. Podmnožina &lt;big&gt;\(B\subseteq A\)&lt;/big&gt; může být svazem, ale nemusí být podsvazem v A.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Konvexní podsvaz ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Nechť (A,∧,∨) je svaz a B je podsvaz A. Pak B&nbsp; se nazývá [[Konvexní množina|konvexní]] podsvaz, je-li &lt;big&gt;\(\forall a,b \in B , c \in A : a \leq c \leq b \Rightarrow c \in B\)&lt;/big&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Neboli podsvaz je konvexní, když s každými dvěma prvky &lt;big&gt;\(a \leq b\)&lt;/big&gt; obsahuje i celý interval [a,b].</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Související články ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Svaz (matematika)|Svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Modulární svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Distributivní svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Úplný svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Externí odkazy ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Článek z Wikipedie}}</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Algebraické struktury]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Algebraické struktury]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Teorie uspořádání]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Teorie uspořádání]]</div></td></tr> </table>

Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Podsvaz&diff=328818&oldid=prev 2013-09-22T13:09:06Z

<p>1 revizi</p> <table style="background-color: white; color:black;"> <tr valign='top'> <td colspan='1' style="background-color: white; color:black;">← Starší verze</td> <td colspan='1' style="background-color: white; color:black;">Verze z 22. 9. 2013, 13:09</td> </tr></table>

Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Podsvaz&diff=328817&oldid=prev 2012-10-23T08:20:30Z

<p>1 revizi</p> <p><b>Nová stránka</b></p><div>{{Wikipedia-cs|Podsvaz|700}}<br /> <br /> [[Kategorie:Algebraické struktury]]<br /> [[Kategorie:Teorie uspořádání]]</div>

Sysop