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Journal of Function Spaces and Applications
Volume 2013, Article ID 925742, 5 pages
Research Article

Homotopy Characterization of ANR Function Spaces

Fakulteta za Matematiko in Fiziko, Jadranska Ulica 19, 1111 Ljubljana, Slovenia

Received 5 May 2013; Accepted 25 August 2013

Academic Editor: Yongsheng S. Han

Copyright © 2013 Jaka Smrekar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be an absolute neighbourhood retract (ANR) for the class of metric spaces and let be a topological space. Let denote the space of continuous maps from to equipped with the compact open topology. We show that if is a compactly generated Tychonoff space and is not discrete, then is an ANR for metric spaces if and only if is hemicompact and has the homotopy type of a CW complex.