Vickers, Steven (2009) The connected Vietoris powerlocale. Topology and its Applications, 156. pp. 18861910. ISSN 01668641
 URL of Published Version: http://www.elsevier.com/locate/topol Identification Number/DOI: http://dx.doi.org/10.1016/j.topol.2009.03.043 The connected Vietoris powerlocale is defined as a strong monad Vc on the category of locales. VcX is a sublocale of Johnstone's Vietoris powerlocale VX, a localic analogue of the Vietoris hyperspace, and its points correspond to the weakly semifitted sublocales of X that are “strongly connected”. A product map ×:VcX×VcY→Vc(X×Y) shows that the product of two strongly connected sublocales is strongly connected. If X is locally connected then VcX is overt. For the localic completion of a generalized metric space Y, the points of are certain Cauchy filters of formal balls for the finite power set with respect to a Vietoris metric.

Type of Work:  Article 

Date:  2009 (Publication) 
School/Faculty:  Schools (1998 to 2008) > School of Computer Science 
Department:  Computer Science 
Subjects:  Q Science (General) QA75 Electronic computers. Computer science QA Mathematics 
Institution:  University of Birmingham 
Copyright Holders:  Elsevier 
ID Code:  182 
Refereed:  YES 
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