Is fixed point property a topological property?
I already came up with some examples, and think the answer may be yes. But I don't know theoretical proof to get that.
2026-04-02 13:22:35.1775136155
Is fixed point property a topological property?
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Let $X$ has fixed-point property and $\phi: X\to Y$ be a homeomorphism. If $f:Y\to Y$ is a continuous function, then $\phi^{-1}\circ f \circ \phi : X\to X$ is also continuous so it has a fixed point, say it $x$. You can easily check that $\phi(x)$ is a fixed point of $f$.