Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	Perfectness in locales
Publication Date:	2016-06-24
Authors:	- Javier Gutiérrez García - Tomasz Kubiak - Jorge Picado
Abstract:	This paper makes a comparison between two notions of perfectness for locales which come as direct reformulations of the two equivalent topological definitions of perfectness. These reformulations are no longer equivalent. It will be documented that a locale may appropriately be called perfect if each of its open sublocales is a join of countably many closed sublocales. Certain circumstances are exhibited in which both reformulations coincide. This paper also studies perfectness in mildly normal locales. It is shown that perfect and mildly normal locales coincide with the Oz locales extensively studied in the last decade.
Institution:	DMUC 16-33
Online version:	http://www.mat.uc.pt/preprints/eng_2016.htm
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