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quasi
Posts:
12,050
Registered:
7/15/05


Re: Onto [0,1]
Posted:
Apr 25, 2013 7:19 PM


Butch Malahide wrote: >quasi wrote: >> Prove or disprove: >> >> If X is a topological space and f: X > [0,1] is a >> continuous surjection, then X has a subspace homeomorphic >> to the Cantor set. > >No, X could have the discrete topology.
So much for that idea.
Perhaps the claim can be fixed (without turning it into a triviality).
quasi



