Homotopy characterization of ANR mapping spaces
Algebraic Topology
2007-08-30 v2 General Topology
Abstract
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).
Cite
@article{arxiv.0708.3697,
title = {Homotopy characterization of ANR mapping spaces},
author = {Jaka Smrekar},
journal= {arXiv preprint arXiv:0708.3697},
year = {2007}
}
Comments
Simplification of proof of Theorem 1.2 and minor changes