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1. 

   A Characterization of the Prime Closed Filter Compactification of a Topological Space

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: H.L. Bentley H. Herrlich

   The prime compactification whose points are the prime closed filters can be defined for a general topological space and is naturally functorial. We derive several properties of this compactification and present a characterization.

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2. 

   Balanced and Closed-generated Filters In Frames

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Themba Dube

   We introduce the notions of balanced filters and closed-generated filters in frames and use them to give a new characterisation of normality for frames, and hence, due to normality being a conservative property, a new characterisation of normality for topological...

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3. 

   Katětov revisited: a frame-theoretic excursion

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Themba Dube

   The Katětov extension of a frame is, as in the case of spaces, compact only for compact completely regular frames. This result is purely topological because, subject to appropriate foundations, compact regular frames are topologies. In this paper we find...

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4. 

   Approximation and Compactness

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: E. Colebunders --- Vrije Universiteit Brussel, België R. Lowen --- Universiteit Antwerpen, België

   In approach theory convergence is described by means of limit and adherence operators acting on filters or ultrafilters. The value of the limit resp. adherence operator on an (ultra)filter in a point x is interpreted as the distance that the...

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