Does $(0,1]$ have Fixed-point property? I can't wrap my head around any examples of continous map $f:(0,1]\rightarrow(0,1]$ that doesn't have fixed point.
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1Note that $(0,1]$ is homeomorphic to $[0,\infty)$ - does that have the fixed point property? (Think about addition ...) – Noah Schweber Mar 07 '21 at 17:05
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1Have you tried to draw any pictures? – Randall Mar 07 '21 at 17:05
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$f:(0,1] \to (0,1]$ defined by $f(x) = \frac{1}{2}x$ has no fixed point.
JLinsta
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well yeah, i thought about those and this map is $f:(0,1]\rightarrow(0,\frac{1}{2}]$ doesnt it have to be $(0,1]\rightarrow(0,1]$? – rubiccube713 Mar 07 '21 at 17:08
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