3
$\begingroup$

Let $X$ be some space, $A$ a subspace of $X$, $f:X \rightarrow X$ a function. My first guess for what $f|A$ is would be that the domain of $f$ is restricted to $A$, but I can't find any confirmation that this is actually the case. The only notation that I'm aware of is $f|_A$.

For reference, the actual place that this question arose in is in Hatcher's Algebraic Topology page 2:

A deformation retraction of a space $X$ onto a subspace $A$ is a family of maps $f_t:X \rightarrow X$, $t \in I$, such that $f_0 = \mathbf{1}$ (the identity map), $f_1(X) = A$, and $f_t|A = \mathbf{1}$ for all $t$.

$\endgroup$
7
$\begingroup$

You are correct, this is indeed just a restriction.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.