I am studying analysis,I met a excercise as following.
note $Homeo([0,1]):=\{f:[0,1]\to [0,1]|f\ is\ continuous\ bijection\}$.
Considers $f,g\in Homeo({0,1})$ which both have two fixed points $1$ and $0$.
Prove exists $h\in Homeo([0,1])$ s.t $h^{-1}fh\equiv g$ .
I have no idea about how to prove it,can sb give me some idea?
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For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to – Sourav Ghosh Aug 15 '22 at 14:26
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Does this answer your question Show two interval homeomorphisms are topologically conjugate – Sourav Ghosh Aug 15 '22 at 14:29
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1yes，great thanks – learning analysis Aug 15 '22 at 16:20