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Recall that a space Y is contractible if the identity map is homotopic to a constant map. Let Y be contractible space and let X be any space. Then, for any maps , .

Proof: Let Y be a contractible space and let X be any space. , where is a constant map. There exists a map such that , for . for some point .

Let be any two maps. Consider where

When , , . Therefore G is cts.

,

.

Therefore .