Completely regular ordered spaces
type: Item
instance of: scholarly article
title: Completely regular ordered spaces
zbMATH Open document ID: 0729.54019
DOI: 10.1007/BF00418656
published in: Order
publication date: 1990-01-01T00:00:00Z
review text: This paper studies a concept introduced in a not yet published paper of \textit{J. D. Lawson}: a strictly completely regular (partially) ordered space. The definition is long; it is said to be equivalent to a definition in a 1968 Edinburgh dissertation by \textit{M. J. Canfell}. Lawson showed that these spaces are completely regular ordered in the sense of \textit{L. Nachbin} [Topology and Order (1965; Zbl 0131.379)], and asked if the converse is true. The author shows that it is not true. However, it becomes true if the space is required to be locally compact, or a topological lattice, or a C-space (i.e. the smallest upper set containing a closed set is closed, and also the smallest lower set containing it).
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 54H12
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 4205376
zbMATH Keywords: pairwise completely regular space
zbMATH Keywords: I-space
zbMATH Keywords: topological lattice
zbMATH Keywords: C-space
author: Hans Peter Künzi
reviewed by: J. R. Isbell
MaRDI profile type: Publication
cites work: Increasing semicontinuous functions and compact topological lattices
cites work: On separation axioms for certain types of ordered topological space
cites work: On Bitopological Compactness
cites work: On Uniform Spaces with a Unique Structure
cites work: Q3966761
cites work: Q3898534
cites work: Bitopological Spaces and Quasi-Uniform Spaces
cites work: Q5575305
cites work: Bicontinuous preordered topological spaces
cites work: Ordered Topological Spaces and the Representation of Distributive Lattices
cites work: Q3833249
full work available at URL: https://doi.org/10.1007/bf00418656
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description: scientific article; zbMATH DE number 4205376