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12:27 PM
was created and removed before. Now it was created again:
2
Q: $X,Y$ be finite topological spaces such that there exist continuous injections from $X$ to $Y$ and $Y$ to $X$ ; are $X$ and $Y$ homeomorphic?

Saun DevDoes the analogue of Schroder-Bernstein hold for finite topological spaces ? i.e. Let $X,Y$ be finite topological spaces such that there exist continuous injections from $X$ to $Y$ and $Y$ to $X$ , then are $X$ and $Y$ homeomorphic ? I know that it isn't true for arbitrary topological spaces ( ev...

Perhaps synonym $\to$ would be reasonable? This would prevent the tag from being repeatedly created and removed agina and again.
Of course, there is a space for discussion whether this could be useful as a standalone tag.
 
 
2 hours later…
2:21 PM
Another question was added to the above tag:
0
Q: If $X$ and $Y$ are homeomorphic, then for every $A\subset X$, $X-A$ and $Y-f(A)$ are homeomorphic.

user338393Let $X$ and $Y$ be metric spaces and $X$ and $Y$ are homeomorphic under $f:X\to Y$, then for every $A\subset X$, $X-A$ and $Y-f(A)$ are homeomorphic. It is quite intuitive but how can we write the proof rigorously? How can we construct the new homeomorphism $g:A-X\to Y-f(A)$? Could anyone plea...

Should it be removed before it grows too much? Or should we discuss this on meta first?
 
 
4 hours later…
6:15 PM
What do you think about adding a tag , et al? I'm fairly new to the subject, and I think I'll be using it more often in coming days!
 

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