The Poset of Perfect Irreducible Images of a Space

Abstract

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.