Range-preserving AE(0)-spaces

W. W. Comfort; A. W. Hager

doi:10.4995/agt.2013.1614

Authors

W. W. Comfort Wesleyan University
A. W. Hager Wesleyan University

DOI:

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

Keywords:

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

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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Author Biographies

W. W. Comfort, Wesleyan University

Department of Mathematics and Computer Science

A. W. Hager, Wesleyan University

Department of Mathematics and Computer Science

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