1. ## 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?

2. 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.