https://topospaces.subwiki.org/w/index.php?action=history&feed=atom&title=Metric_induces_proximity_structrureMetric induces proximity structrure - Revision history2026-07-13T09:03:55ZRevision history for this page on the wikiMediaWiki 1.41.2https://topospaces.subwiki.org/w/index.php?title=Metric_induces_proximity_structrure&diff=2711&oldid=prevVipul: New page: ==Statement== Suppose <math>(X,d)</math> is a fact about::metric space. <math>X</math> can be given the structure of a fact about::proximity space with the following proximity rel...2008-11-24T21:09:26Z<p>New page: ==Statement== Suppose <math>(X,d)</math> is a <a href="/w/index.php?title=Fact_about::metric_space&action=edit&redlink=1" class="new" title="Fact about::metric space (page does not exist)">fact about::metric space</a>. <math>X</math> can be given the structure of a <a href="/w/index.php?title=Fact_about::proximity_space&action=edit&redlink=1" class="new" title="Fact about::proximity space (page does not exist)">fact about::proximity space</a> with the following proximity rel...</p>
<p><b>New page</b></p><div>==Statement==<br />
<br />
Suppose <math>(X,d)</math> is a [[fact about::metric space]]. <math>X</math> can be given the structure of a [[fact about::proximity space]] with the following proximity relation:<br />
<br />
<math>A \delta B \iff d(A,B) = 0</math>.<br />
<br />
==Related facts==<br />
<br />
* [[Metric induces topology]]<br />
* [[Metric induces uniform structure]]</div>Vipul