https://subwiki.org/w/index.php?action=history&feed=atom&title=Topological_dimension 2026-04-17T14:48:15Z Revision history for this page on the wiki MediaWiki 1.41.2 https://subwiki.org/w/index.php?title=Topological_dimension&diff=73&oldid=prev 2008-06-08T12:20:38Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:20, 8 June 2008</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>&lt;noinclude&gt;[[Status::Standard non-basic definition| ]][[Topic::Point-set topology| ]][[Primary wiki::Topospaces| ]]&lt;/noinclude&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>&lt;noinclude&gt;[[Status::Standard non-basic definition| ]][[Topic::Point-set topology| ]][[Primary wiki::Topospaces| ]]&lt;/noinclude&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>''Topological dimension''': The '''topological dimension''' or '''covering dimension''' or '''Lebesgue covering dimension''' of a [[topological space]] is defined as the smallest integer &lt;math&gt;m&lt;/math&gt; such that any [[open cover]] of the topological space has an open [[refinement]] that has [[order of a collection of subsets|order]] at most &lt;math&gt;m + 1&lt;/math&gt;.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;">'</ins>''Topological dimension''': The '''topological dimension''' or '''covering dimension''' or '''Lebesgue covering dimension''' of a [[topological space]] is defined as the smallest integer &lt;math&gt;m&lt;/math&gt; such that any [[open cover]] of the topological space has an open [[refinement]] that has [[order of a collection of subsets|order]] at most &lt;math&gt;m + 1&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Primary subject wiki entry: [[Topospaces:Topological dimension]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Primary subject wiki entry: [[Topospaces:Topological dimension]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Also located at: [[Wikipedia:Lebesgue covering dimension]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Also located at: [[Wikipedia:Lebesgue covering dimension]]</div></td></tr> </table>

Vipul https://subwiki.org/w/index.php?title=Topological_dimension&diff=72&oldid=prev 2008-06-08T12:20:24Z

<p>New page: &lt;noinclude&gt;<a href="/w/index.php?title=Status::Standard_non-basic_definition&amp;action=edit&amp;redlink=1" class="new" title="Status::Standard non-basic definition (page does not exist)"> </a><a href="/w/index.php?title=Topic::Point-set_topology&amp;action=edit&amp;redlink=1" class="new" title="Topic::Point-set topology (page does not exist)"> </a><a href="/w/index.php?title=Primary_wiki::Topospaces&amp;action=edit&amp;redlink=1" class="new" title="Primary wiki::Topospaces (page does not exist)"> </a>&lt;/noinclude&gt; &#039;&#039;Topological dimension&#039;&#039;&#039;: The &#039;&#039;&#039;topological dimension&#039;&#039;&#039;...</p> <p><b>New page</b></p><div>&lt;noinclude&gt;[[Status::Standard non-basic definition| ]][[Topic::Point-set topology| ]][[Primary wiki::Topospaces| ]]&lt;/noinclude&gt;<br /> <br /> &#039;&#039;Topological dimension&#039;&#039;&#039;: The &#039;&#039;&#039;topological dimension&#039;&#039;&#039; or &#039;&#039;&#039;covering dimension&#039;&#039;&#039; or &#039;&#039;&#039;Lebesgue covering dimension&#039;&#039;&#039; of a [[topological space]] is defined as the smallest integer &lt;math&gt;m&lt;/math&gt; such that any [[open cover]] of the topological space has an open [[refinement]] that has [[order of a collection of subsets|order]] at most &lt;math&gt;m + 1&lt;/math&gt;.<br /> <br /> Primary subject wiki entry: [[Topospaces:Topological dimension]]<br /> <br /> Also located at: [[Wikipedia:Lebesgue covering dimension]]</div>

Vipul