Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Onto [0,1]
Posted:
Apr 25, 2013 6:39 PM


On Apr 25, 5:19 pm, quasi <qu...@null.set> wrote: > Prove or disprove: > > If X is a topological space and f: X > [0,1] is a > continuous surjection, then X has a subspace C homeomorphic > to the Cantor set and such that f(C) = [0,1].
If X = [0,1] and f(x) = x, then X has a subspace C homeomorphic to the Cantor set, but f(C) is not equal to [0,1].



