Algebra, Logic and Topology

 

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Author(s)
Maria Manuel Clementino; Walter Tholen;

Title
A characterization of the Vietoris Topology

Abstract
The Vietoris topology on the hyperspace VX of closed subsets of a topological space X is shown to represent the closed-valued, clopen relations with codomain $X$. Hence, it is characterized by a (co)universal property which can be formulated in concrete categories equipped with a closure operator. Functorial properties of the Vietoris topology are derived, and some examples of closure-structured categories with Vietoris objects are exhibited.

Journal
Topology Proceedings

Volume
22

Year
1997

Issue

Page(s)
71-95

 
     
 

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