Homotopy Characterization of Anr Mapping Spaces
نویسنده
چکیده
Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let Y X denote the space of continuous maps from X to Y equipped with the compact open topology. It is shown that if X is a CW complex then Y X is an ANR for the class of metric spaces if and only if Y X 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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