2
$\begingroup$

Give an example of a function $f:X \to Y$ and a subset $A \subset X$ such that f is open but $f_A$, the restriction of $f$ to $A$ is not open.

Can someone help me please? Thanks

$\endgroup$
  • $\begingroup$ what do you mean by f is open? $\endgroup$ – RowanS Jun 21 '15 at 19:40
  • $\begingroup$ @Rowan: It’s a standard notion: it means that if $U$ is open in the domain of $f$, then $f[U]$ is open in the codomain. $\endgroup$ – Brian M. Scott Jun 21 '15 at 19:44
7
$\begingroup$

HINT: Let $X=Y=\Bbb R$, take $f$ to be the identity function, and take $A$ to be a set that isn’t open in $X$.

$\endgroup$
  • $\begingroup$ Thanks, the example was easy to find $\endgroup$ – Ryoma Jun 21 '15 at 19:53
  • $\begingroup$ @Ryoma: You’re welcome. $\endgroup$ – Brian M. Scott Jun 21 '15 at 19:55
  • 1
    $\begingroup$ @Ryoma: If you feel that this answer has satisfied your question, it is encouraged that you accept the answer. Since you haven't accepted any answers before (as of now), I thought I'd point out this link for your information. $\endgroup$ – Prism Jun 22 '15 at 5:06

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.