http://wiki.karljones.com/index.php?action=history&feed=atom&title=Metric_space 2026-10-23T19:16:50Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Metric_space&diff=18675&oldid=prev 2016-09-21T21:48:39Z

<p>Created page with &quot;In <a href="/index.php/Mathematics" title="Mathematics">mathematics</a>, a &#039;&#039;&#039;metric space&#039;&#039;&#039; is a <a href="/index.php/Set_(mathematics)" title="Set (mathematics)">set</a> for which <a href="/index.php?title=Distance&amp;action=edit&amp;redlink=1" class="new" title="Distance (page does not exist)">distances</a> between all <a href="/index.php/Element_(mathematics)" title="Element (mathematics)">members</a> of the Set (mathematic...&quot;</p> <p><b>New page</b></p><div>In [[mathematics]], a '''metric space''' is a [[Set (mathematics)|set]] for which [[Distance|distances]] between all [[Element (mathematics)|members]] of the [[Set (mathematics)|set]] are defined.<br /> <br /> Those distances, taken together, are called a [[Metric (mathematics)|metric]] on the set.<br /> <br /> == Description ==<br /> <br /> A metric on a space induces [[Topological property|topological properties]] like [[Open set|open]] and [[Closed set|closed sets]], which lead to the study of more abstract [[Topological space|topological spaces]].<br /> <br /> The most familiar metric space is 3-dimensional [[Euclidean space]]. In fact, a &quot;metric&quot; is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them.<br /> <br /> Other metric spaces occur for example in [[elliptic geometry]] and [[hyperbolic geometry]], where distance on a sphere measured by angle is a metric, and the hyperboloid model of hyperbolic geometry is used by special relativity as a metric space of velocities.<br /> <br /> == See also ==<br /> <br /> * [[Aleksandrov–Rassias problem]]<br /> * [[Category of metric spaces]]<br /> * [[Classical Wiener space]]<br /> * [[Glossary of Riemannian and metric geometry]]<br /> * [[Hilbert space]]<br /> * [[Isometry, contraction mapping and metric map]]<br /> * [[Lipschitz continuity]]<br /> * [[Measure (mathematics)]]<br /> * [[Metric (mathematics)]]<br /> * [[Metric signature]]<br /> * [[Metric tensor]]<br /> * [[Metric tree]]<br /> * [[Norm (mathematics)]]<br /> * [[Normed vector space]]<br /> * [[Product metric]]<br /> * [[Space (mathematics)]]<br /> * [[Triangle inequality]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Metric_space Metric space] @ Wikipedia<br /> <br /> [[Category:Mathematics]]</div>

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