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Topic: Onto [0,1]
Replies: 40   Last Post: Apr 29, 2013 10:16 PM

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Posts: 12,067
Registered: 7/15/05
Re: Onto [0,1]
Posted: Apr 25, 2013 6:33 PM
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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.


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