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    Nullhomotopic Mappings and Contractible Spaces

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    I am having problems proving this fact. A space X is contractible if and only if
    every map f:X to Y (Y is arbitrary) is nullhomotopic. Similarly show X is contractible
    iff ever map f:Y to X is nullhomotopic.

    In the first case if Y=X then see that the identity map on X is nullhomotopic. But Im not
    sure how to proceed for the rest.

    © BrainMass Inc. brainmass.com June 3, 2020, 7:49 pm ad1c9bdddf

    Solution Preview

    Notation: We let c_x:X ->{x} denote the constant map to {x}.
    "o" is composition, "~" is "homotopic to", $1_X$ identity on X

    Suppose that X is ...

    Solution Summary

    Nullhomotopic Mappings and Contractible Spaces are investigated.