Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces
type: Item
instance of: scholarly article
title: Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces
zbMATH Open document ID: 0697.46010
DOI: 10.1007/BF01200092
author: Aaron R. Todd
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: Certain topological properties of a completely regular Hausdorff space T characterize functional analytic properties of the locally convex space C(T) of continuous real (complex) valued functions on T under the compact-open topology. Such characterizations have been central in distinguishing closely related properties of locally convex linear topological spaces. The question of such a characterization remains open for the following topological property: Each pseudocompact subset of T is relatively compact. However, this leads naturally to a new topological property characterizing an infrabarrelled type property of C(T). Distinguishing examples and further open questions are included.
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46A50
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 4142772
zbMATH Keywords: Warner bounded
zbMATH Keywords: bornivorous
zbMATH Keywords: topological properties of a completely regular Hausdorff space T characterize functional analytic properties of the locally convex space C(T)
zbMATH Keywords: compact-open topology
zbMATH Keywords: pseudocompact subset
zbMATH Keywords: infrabarrelled type property
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01200092
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description: scientific article; zbMATH DE number 4142772