Range-preserving AE(0)-spaces

W. W. Comfort

United States

Wesleyan University

Department of Mathematics and Computer Science

A. W. Hager

United States

Wesleyan University

Department of Mathematics and Computer Science

Submitted: 2013-07-25

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Accepted: 2013-07-25

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Published: 2013-07-25

DOI: https://doi.org/10.4995/agt.2013.1614
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Keywords:

Absolute extensor, Retraction, Zero-dimensional space, Range- preserving function, Dugundji space, Dyadic space, Countable chain condition

Supporting agencies:

This research was not funded

Abstract:

All spaces here are Tychonoff spaces. The class AE(0) consists of those spaces which are absolute extensors for compact zero-dimensional spaces. We define and study here the subclass AE(0)rp, consisting of those spaces for which extensions of continuous functions can be chosen to have the same range. We prove these results. If each point of T 2 AE(0) is a G-point of T , then T 2 AE(0)rp. These are equivalent: (a) T 2 AE(0)rp; (b) every compact subspace of T is metrizable; (c) every compact subspace of T is dyadic; and (d) every subspace of T is AE(0). Thus in particular, every metrizable space is an AE(0)rp-space.
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