Vol. 91, No. 1, 1980

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Every space is a path component space

Douglas Harris

Vol. 91 (1980), No. 1, 95–104
Abstract

It is shown that every topological space appears as quotient of a paracompact Hausdorff space in a very natural way: as the space of path components. This means that the “pathology” of closure operators in non-Hausdorff spaces appears as “pathology” of path components in spaces which have “nice” closure operators.

Mathematical Subject Classification 2000
Primary: 54B15
Milestones
Received: 19 April 1976
Revised: 18 December 1977
Published: 1 November 1980
Authors
Douglas Harris