0
$\begingroup$

An example of a space $X$ that is not homotopy equivalent to a point, but there exists a $p \in X$ such that $X \backslash \{p\}$ is homotopy equivalent to a point.

$\endgroup$
1
  • 4
    $\begingroup$ Two points works $\endgroup$
    – Thomas Rot
    Apr 18 '20 at 18:11
6
$\begingroup$

Hint: How about $S^1$? Not "homotopy equivalent to a point" you have via the fundamental group $\pi_1(S^1) = \mathbb{Z}$ for example, so now what about the complement of a point? At least intuitively it should be clear why this example works.

$\endgroup$

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.