Does 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 homeomorphism $\to$ general-topology 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.
Let $X$ 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...
What do you think about adding a tag pseudocode, efficiency-of-algorithm et al? I'm fairly new to the subject, and I think I'll be using it more often in coming days!
