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class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></span></li></ul>This article is within the scope of <b><a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">WikiProject Mathematics</a></b>, a collaborative effort to improve the coverage of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> on Wikipedia. If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Mathematics" title="Wikipedia talk:WikiProject Mathematics">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Mathematics</span><span class="wpb-project_link">Wikipedia:WikiProject Mathematics</span><span class="wpb-banner_name">Template:WikiProject Mathematics</span><span class="wpb-assessment_cat">mathematics articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-low"><a href="/wiki/Category:Low-priority_mathematics_articles" title="Category:Low-priority mathematics articles">Low</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>Low-priority</b> on the <a href="/wiki/Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Assessment#Priority_scale" class="mw-redirect" title="Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Assessment">project's priority scale</a>.</td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="untitled" data-mw-thread-id="h-untitled-2007-10-05T09:25:00.000Z"><span data-mw-comment-start="" id="h-untitled-2007-10-05T09:25:00.000Z"></span>untitled<span data-mw-comment-end="h-untitled-2007-10-05T09:25:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:History_of_the_separation_axioms&action=edit&section=1" title="Edit section: untitled"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Charles_Matthews-2007-10-05T09:25:00.000Z-untitled"></span>Yes, I <i>am</i> working on this. — <a href="/wiki/User:Toby_Bartels" title="User:Toby Bartels">Toby</a> 02:41 Aug 9, 2002 (PDT) </p><p>Thanks, this looks like a good start. We might consider doing a table outlining the various common definition sets that are in use, such as Willard's and Steen and Seebach's. Then again, maybe it would get to cluttered to be useful. -- <a href="/wiki/User:Fropuff" title="User:Fropuff">Fropuff</a> 15:36, 2005 Feb 8 (UTC) </p> <dl><dd><dl><dd>Reference to Wikipedia should be avoided (<a href="/wiki/Wikipedia:SELF" class="mw-redirect" title="Wikipedia:SELF">WP:SELF</a>). <a href="/wiki/User:Charles_Matthews" title="User:Charles Matthews">Charles Matthews</a> <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Charles_Matthews-2007-10-05T09:25:00.000Z-untitled" class="ext-discussiontools-init-timestamplink">09:25, 5 October 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Charles_Matthews-2007-10-05T09:25:00.000Z-untitled"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Charles_Matthews-2007-10-05T09:25:00.000Z-untitled"></span></dd></dl></dd></dl> <p><span data-mw-comment-start="" id="c-41.241.91.225-2008-11-28T22:05:00.000Z-untitled"></span>Surely a merger with the Separation Axioms article is in order? <span style="font-size: smaller;" class="autosigned">—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/41.241.91.225" title="Special:Contributions/41.241.91.225">41.241.91.225</a> (<a href="/wiki/User_talk:41.241.91.225" title="User talk:41.241.91.225">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-41.241.91.225-2008-11-28T22:05:00.000Z-untitled" class="ext-discussiontools-init-timestamplink">22:05, 28 November 2008 (UTC)</a></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-41.241.91.225-2008-11-28T22:05:00.000Z-untitled"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-41.241.91.225-2008-11-28T22:05:00.000Z-untitled"></span> </p><p><span data-mw-comment-start="" id="c-Toby_Bartels-2009-07-13T20:50:00.000Z-untitled"></span>On the contrary, this was split <i>out</i> of <a href="/wiki/Separation_axiom" title="Separation axiom">Separation axiom</a> to avoid confusing readers about the different definitions. (See <a class="external text" href="https://secure.wikimedia.org/wikipedia/en/w/index.php?title=Separation_axioms&oldid=140430">this old version</a> for what that could look like.) The problem is that it's not clear to me how much can even be written about this without <a href="/wiki/Wikipedia:OR" class="mw-redirect" title="Wikipedia:OR">original research</a>, which is why I haven't been able to finish it. —<a href="/wiki/User:Toby_Bartels" title="User:Toby Bartels">Toby Bartels</a> (<a href="/wiki/User_talk:Toby_Bartels" title="User talk:Toby Bartels">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Toby_Bartels-2009-07-13T20:50:00.000Z-untitled" class="ext-discussiontools-init-timestamplink">20:50, 13 July 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Toby_Bartels-2009-07-13T20:50:00.000Z-untitled"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Toby_Bartels-2009-07-13T20:50:00.000Z-untitled"></span> </p><p><span data-mw-comment-start="" id="c-Toby_Bartels-2009-07-24T19:31:00.000Z-untitled"></span>One possibility would be to merge an abbreviated form of this into <a href="/wiki/Separation_axiom" title="Separation axiom">Separation axiom</a> as a new section, towards the bottom, on terminological variations. Potentially, that could even include the table that Fropuff called for above, but it would not have a whole history. Until the history can be written without OR, that may be the best thing to do, although I'm not up to doing it myself yet. —<a href="/wiki/User:Toby_Bartels" title="User:Toby Bartels">Toby Bartels</a> (<a href="/wiki/User_talk:Toby_Bartels" title="User talk:Toby Bartels">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Toby_Bartels-2009-07-24T19:31:00.000Z-untitled" class="ext-discussiontools-init-timestamplink">19:31, 24 July 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Toby_Bartels-2009-07-24T19:31:00.000Z-untitled"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Toby_Bartels-2009-07-24T19:31:00.000Z-untitled"></span> </p><p><span data-mw-comment-start="" id="c-Toby_Bartels-2011-12-31T06:23:00.000Z-untitled"></span>So I just rated my own abandoned page, moderately. —<a href="/wiki/User:Toby_Bartels" title="User:Toby Bartels">Toby Bartels</a> (<a href="/wiki/User_talk:Toby_Bartels" title="User talk:Toby Bartels">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Toby_Bartels-2011-12-31T06:23:00.000Z-untitled" class="ext-discussiontools-init-timestamplink">06:23, 31 December 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Toby_Bartels-2011-12-31T06:23:00.000Z-untitled"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Toby_Bartels-2011-12-31T06:23:00.000Z-untitled"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Contradiction_in_terms" data-mw-thread-id="h-Contradiction_in_terms-2013-02-15T11:09:00.000Z"><span data-mw-comment-start="" id="h-Contradiction_in_terms-2013-02-15T11:09:00.000Z"></span>Contradiction in terms<span data-mw-comment-end="h-Contradiction_in_terms-2013-02-15T11:09:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:History_of_the_separation_axioms&action=edit&section=2" title="Edit section: Contradiction in terms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Espen180-2013-02-15T11:09:00.000Z-Contradiction_in_terms"></span>The last sentence in "Origins" reads </p> <pre> For example, a regular space (called T3) does not have to be a Hausdorff space (called T2), at least not according to the simplest definition of regular spaces. </pre> <p>All the sources I can find state the T3 axiom as (T1 and regular), which is equivalent to regular Hausdorff. It may well be possible that there is an example of "Tj does not imply Ti, even though i<j", but this example is simply confusing. I think the example given of "T3 does not imply T2" should either be changed or removed completely. <a href="/w/index.php?title=User:Espen180&action=edit&redlink=1" class="new" title="User:Espen180 (page does not exist)">Espen180</a> (<a href="/w/index.php?title=User_talk:Espen180&action=edit&redlink=1" class="new" title="User talk:Espen180 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Espen180-2013-02-15T11:09:00.000Z-Contradiction_in_terms" class="ext-discussiontools-init-timestamplink">11:09, 15 February 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Espen180-2013-02-15T11:09:00.000Z-Contradiction_in_terms"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Espen180-2013-02-15T11:09:00.000Z-Contradiction_in_terms"></span> </p><p><span data-mw-comment-start="" id="c-Toby_Bartels-2013-05-25T21:31:00.000Z-Contradiction_in_terms"></span>The reality <i>is</i> confusing, that's the point. For a reference in which T<sub>3</sub> need not be T<sub>2</sub>, see Steen & Seebach (cited in the article). --<a href="/wiki/User:Toby_Bartels" title="User:Toby Bartels">Toby Bartels</a> (<a href="/wiki/User_talk:Toby_Bartels" title="User talk:Toby Bartels">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:History_of_the_separation_axioms#c-Toby_Bartels-2013-05-25T21:31:00.000Z-Contradiction_in_terms" class="ext-discussiontools-init-timestamplink">21:31, 25 May 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Toby_Bartels-2013-05-25T21:31:00.000Z-Contradiction_in_terms"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Toby_Bartels-2013-05-25T21:31:00.000Z-Contradiction_in_terms"></span> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Talk:History_of_the_separation_axioms&oldid=1202734683">https://en.wikipedia.org/w/index.php?title=Talk:History_of_the_separation_axioms&oldid=1202734683</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Start-Class_mathematics_articles" title="Category:Start-Class mathematics articles">Start-Class mathematics articles</a></li><li><a href="/wiki/Category:Low-priority_mathematics_articles" title="Category:Low-priority mathematics articles">Low-priority mathematics articles</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 3 February 2024, at 11:16<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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