Let $X,Y$ be metric spaces.
Suppose that there is a mapping $f:X\to Y$ which is bijective and continuous.
Suppose that there is a mapping $g:Y\to X$ which is bijective and continuous.
Then, are $X$ and $Y$ homeomorphic?
2026-05-05 17:41:34.1778002894
$f:X\to Y$ and $g:Y\to X$ are bijective and continuous. Then two metric spaces $X$ and $Y$ are homeomorphic?
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