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Compactifications of partial frames via strongly regular ideals

  • John Frith EMAIL logo and Anneliese Schauerte
From the journal Mathematica Slovaca

Abstract

Partial frames provide a fertile context in which to do pointfree structured and unstructured topology, using a small collection of axioms of an elementary nature. Amongst other things they can be used to investigate similarities and differences between frames, σ-frames and κ-frames.

In this paper, the theory of strong inclusions for partial frames is used to describe compactifications of completely regular partial frames; the elements of these compactifications are given explicitly as strongly regular ideals. This is independent of and encompasses the theory of compactifications for frames. As an application, we revisit the Samuel compactification of a uniform partial frame.


Communicated by Aleš Pultr


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Received: 2015-12-7
Accepted: 2016-6-8
Published Online: 2018-3-31
Published in Print: 2018-4-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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