Homotopy characterization of ANR mapping spaces - Mathematics > Algebraic TopologyReport as inadecuate




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Abstract: Let Y be an absolute neighborhood retract ANR for the class of metricspaces and let X be a Hausdorff space. Let mapX,Y denote the space ofcontinuous maps from X to Y with the compact open topology. It is shown that ifX is a CW complex then mapX,Y is an ANR for the class of metric spaces if andonly if mapX,Y is metrizable and has the homotopy type of a CW complex. Thesame holds also when X is a compactly generated hemicompact spacemetrizability assumption is void in this case.



Author: Jaka Smrekar

Source: https://arxiv.org/







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