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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- Oct 30th 2010, 05:50 AMSogancontinuous 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? - Oct 30th 2010, 10:57 AMemakarov
I believe that a section (see also here) is a right inverse of a given function. That is, $\displaystyle \displaystyle s$ is a section of $\displaystyle \displaystyle f$ is $\displaystyle f \circ s = \mathrm{id}$. 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.