1 Ocak 2017 Dergi makalesi Açık Erişim

Gillam, W. D.; Karan, A.

Dublin Core

<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>Gillam, W. D.</dc:creator>
  <dc:creator>Karan, A.</dc:creator>
  <dc:date>2017-01-01</dc:date>
  <dc:description>In 1914, F. Hausdorff defined a metric on the set of closed subsets of a metric space X. This metric induces a topology on the set H of compact subsets of X, called the Hausdorff topology. We show that the topological space H represents the functor on the category of sequential topological spaces taking T to the set of closed subspaces Z of T x X for which the projection pi(1) : Z -&gt; T is open and proper. In particular, the Hausdorff topology on H depends on the metric space X only through the underlying topological space of X. The Hausdorff space H provides an analog of the Hilbert scheme in topology. As an example application, we explore a certain quotient construction, called the Hausdorff quotient, which is the analog of the Hilbert quotient in algebraic geometry. (C) 2017 Elsevier B.V. All rights reserved.</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/111146</dc:identifier>
  <dc:identifier>oai:zenodo.org:111146</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>TOPOLOGY AND ITS APPLICATIONS 232 102-111</dc:source>
  <dc:title>The Hausdorff topology as a moduli space</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
</oai_dc:dc>