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The Poset of Perfect Irreducible Images of a Space

Published online by Cambridge University Press:  20 November 2018

Jack R. Porter  and
R. Grant Woods
Jack R. Porter
Affiliation:
The University of Kansas, Lawrence, Kansas
R. Grant Woods
Affiliation:
The University of Manitoba, Winnipeg, Manitoba
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We begin by briefly summarizing the contents of this paper; details, and some definitions of terminology, appear in subsequent sections. All hypothesized topological spaces are assumed to be Hausdorff. The reader is referred to [13] for undefined notation and terminology.

A perfect irreducible continuous surjection is called a covering map. Let X be a space, let f and g be two such functions with domain X, and let Rf denote the range of (i.e., the set f [Z]). Then f and g are said to be equivalent (denoted f≈ g) if there is a homeomorphism h : Rf —” Rg such that h of = g. We identify equivalent covering maps with domain X, and then denote by IP(X) the set of such covering maps.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 2 , 01 April 1989 , pp. 213 - 233
Copyright
Copyright © Canadian Mathematical Society 1989

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