https://en.formulasearchengine.com/index.php?title=William_Houlder_Zachariasen&feed=atom&action=historyWilliam Houlder Zachariasen - Revision history2024-03-29T08:27:24ZRevision history for this page on the wikiMediaWiki 1.42.0-wmf.5https://en.formulasearchengine.com/index.php?title=William_Houlder_Zachariasen&diff=28560&oldid=preven>Suslindisambiguator at 12:38, 28 September 20132013-09-28T12:38:52Z<p></p>
<p><b>New page</b></p><div>In the [[mathematics|mathematical branch]] of [[topology]], a '''hyperspace''' (or a space equipped with a hypertopology) is a [[topological space]], which consists of the set ''CL(X)'' of all [[Closed set|closed]] subsets of another topological space ''X'', equipped with a topology so that the [[canonical map]] <br />
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<math>i : x \mapsto \overline{\{x\}},</math><br />
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is a [[homeomorphism]] onto its image. As a consequence, a copy of the original space ''X'' lives inside hyperspace ''CL(X)''. <ref>{{cite journal|last=Lucchetti|first=Roberto|coauthors=Angela Pasquale|title=A New Approach to a Hyperspace Theory|journal=Journal of Convex Analysis|year=1994|volume=1|issue=2|pages=173–193|url=http://www.heldermann-verlag.de/jca/jca01/jca01013.pdf|accessdate=20 January 2013}}</ref> <br />
<ref>{{cite book|last=Beer|first=G.|title=Topologies on closed and closed convex sets|year=1994|publisher=Kluwer Academic Publishers}}</ref><br />
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Early examples of hypertopology include the [[Hausdorff distance|Hausdorff metric]]<ref>{{cite book|last=Hausdorff|first=F.|title=Mengenlehre|year=1927|publisher=W. de Gruyter|location=Berlin and Leipzig}}</ref> and [[Topological space#Topological constructions|Vietoris topology]].<ref>{{cite journal|last=Vietoris|first=L.|title=Stetige Mengen|journal=Monatsh. Fur Math. Und Phys.|year=1921|volume=31|pages=173–204|doi=10.1007/BF01702717}}</ref><br />
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== References ==<br />
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{{Reflist}}<br />
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== External links ==<br />
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[http://rendiconti.dmi.units.it/volumi/22/12.pdf Comparison of Hypertopologies]<br />
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[[Category:Topology]]<br />
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