Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete. then YX is an ANR for metric spaces if and only if X is hemicompact and YX has the homotopy typ... https://www.soiebiologique.com/