Homotopy characterization of ANR mapping spaces

Details Homotopy characterization of ANR mapping spaces Homotopy characterization of ANR mapping spaces

2007-08-27

arxiv.org/abs/0708.3697v2

Mathematics

Algebraic Topology

Simplification of proof of Theorem 1.2 and minor changes

Scientific paper

Let Y be an absolute neighborhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let map(X,Y) denote the space of continuous maps from X to Y with the compact open topology. It is shown that if X is a CW complex then map(X,Y) is an ANR for the class of metric spaces if and only if map(X,Y) is metrizable and has the homotopy type of a CW complex. The same holds also when X is a compactly generated hemicompact space (metrizability assumption is void in this case).

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