2
$\begingroup$

If there are continuous surjections $f: X \to Y$ and $g: Y \to X$ are $X, Y$ homeomorphic? This is not homework. Just to trying to review some topology.

$\endgroup$
6
$\begingroup$

Hint: Let $X=\mathbb{S}^1$ and $Y=[0,1]$.

| cite | improve this answer | |
$\endgroup$
1
$\begingroup$

See for even stronger examples the answers to https://mathoverflow.net/questions/30661/non-homeomorphic-spaces-that-have-continuous-bijections-between-them

| cite | improve this answer | |
$\endgroup$

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