Range - preserving AE ( 0 ) - spaces
نویسنده
چکیده
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), 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 ∈ AE(0) is a Gδ-point of T , then T ∈ AE(0) . These are equivalent: (a) T ∈ AE(0); (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)space. 2010 MSC: Primary 54C55. Secondary 06F20, 46E10, 54E18
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