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Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology

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Morón, Manuel A. and González Gómez, A. (2007) Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology. Topology and its Applications, 154 (10). pp. 2142-2153. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864107000211


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Abstract

In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the Cˇ ech–Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject.


Item Type:Article
Uncontrolled Keywords:Upper semifinite topology; Compactness; Cech–Stone compactification; Fixed point proper
Subjects:Sciences > Mathematics > Topology
ID Code:20316
Deposited On:07 Mar 2013 12:41
Last Modified:12 Dec 2018 15:13

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