Pointfree pseudocompactness revisited
type: Item
instance of: scholarly article
title: Pointfree pseudocompactness revisited
zbMATH Open document ID: 1171.06004
author: Themba Dube
author: Phethiwe Matutu
published in: Topology and its Applications
publication date: 2007-06-26T00:00:00Z
review text: The concept of pseudocompactness in the setting of pointfree topology, due to \textit{D. Baboolal} and \textit{B. Banaschewski} [``Compactification and local connectedness of frames'', J. Pure Appl. Algebra 70, No.~1--2, 3--16 (1991; Zbl 0722.54031)], is studied in detail in this paper. Several internal and also external characterizations of pseudocompactness for general frames are given. Some of these are pointfree extensions of analogous characterizations in topological spaces due to \textit{R. M. Stephenson jun.} [``Pseudocompact spaces'', Trans. Am. Math. Soc. 134, 437--448 (1968; Zbl 0169.53903)]. Nicely, in the case of internal characterizations, whereas the proofs of Stephenson use external tools like maps into the reals, all the proofs in the present paper use only things residing within the frames in question, with no reference to the reals.
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 5167603
zbMATH Keywords: frame
zbMATH Keywords: paracompactness
zbMATH Keywords: countable compactness
zbMATH Keywords: pseudocompactness
zbMATH Keywords: pointfree topology
MaRDI profile type: Publication
full work available at URL: j.topol.2006.01.016
OpenAlex ID: W2046625483
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DOI: 10.1016/J.TOPOL.2006.01.016
description: scientific article; zbMATH DE number 5167603