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Math Help - continuous section

  1. #1
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    continuous section

    Hello,

    I should show that a surjective, continuous map f:X->Y is an identification if it admits a section s:Y->X.

    I don't understand the part: "it admits a section s:Y->X." what does this mean?

    what is a section?
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  2. #2
    MHF Contributor
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    I believe that a section (see also here) is a right inverse of a given function. That is, \displaystyle s is a section of \displaystyle f is f \circ s = \mathrm{id}. Sometimes a section is defined as a function that has a left inverse (so it itself is a right inverse).

    Correspondingly, "to admit a section" means to have a right inverse.
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