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No, even if Y=[0,1]$Y=[0,1]$. The piecewise linear continuous nondecreasing surjection $f:[0,1] \rightarrow [0,1]$ which maps [1/3,2/3]$[1/3,2/3]$ to 1/2$1/2$ and is otherwise 1-1 and linear has no continuous section.
No, even if Y=[0,1]. The piecewise linear continuous nondecreasing surjection $f:[0,1] \rightarrow [0,1]$ which maps [1/3,2/3] to 1/2 and is otherwise 1-1 and linear has no continuous section.
No, even if $Y=[0,1]$. The piecewise linear continuous nondecreasing surjection $f:[0,1] \rightarrow [0,1]$ which maps $[1/3,2/3]$ to $1/2$ and is otherwise 1-1 and linear has no continuous section.
No, even if Y=[0,1]. The piecewise linear continuous nondecreasing surjection $f:[0,1] \rightarrow [0,1]$ which maps [1/3,2/3] to 1/2 and is otherwise 1-1 and linear has no continuous section.
