Range-preserving AE(0)-spaces

W.W. Comfort, A.W. Hager

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.

Keywords

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

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Universitat Politècnica de València

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