A Subcategory of FIL

Ákos Császár

A chapter in Categorical Topology, 1996, pp 241-244 from Springer

Abstract: Abstract It is well-known that a filter space on a set X is a pair $$(x,\mathfrak{S})\,where\,\mathfrak{S}$$ is a collection $$\phi \,\mathfrak{S} \ne \subset \,Fil\,X$$ such that $$\mathbb{X} \in \mathfrak{S}\,for \mathcal{X} \in \mathcal{X}$$ (1) $$S \in \mathfrak{S},S \subset s \in Fil X imply s \in \mathfrak{S}$$ (2) Here Fil X is the set of all (proper or improper) filters in X and x is the ultrafilter fixed at x. A collection $$\mathfrak{S}$$ of this kind can be called a screen on X (see e.g. [2]).

Keywords: 54E17; (54B30); Filter space; screen; Chauchy space; M-screen; chain-complete screen (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-94-009-0263-3_21

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