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quasi
Posts:
12,048
Registered:
7/15/05


Re: Onto [0,1]
Posted:
Apr 25, 2013 6:33 PM


quasi wrote: >William Elliot wrote: >> >>Can an uncountable compact Hausdorff be continuously mapped >>onto [0,1]? > >This has already been answered by David Ullrich (with >improvements Butch Malahide)
Sorry  I hit post button too early.
Continuing ...
A followup question.
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.
quasi



