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

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Bacle H

Posts: 283
Registered: 4/8/12
Re: Onto [0,1]
Posted: Apr 21, 2013 11:07 PM
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On Sunday, April 21, 2013 6:13:15 PM UTC-7, William Elliot wrote:
> On Sun, 21 Apr 2013, wrote:

> > On Sunday, April 21, 2013 12:56:53 AM UTC-7, William Elliot wrote:

> > > Can an uncountable compact Hausdorff be continuously mapped onto [0,1]?
> >
> > Isn't every compact metric space the continuous image of the Cantor set?
> >
> Yes; is every compact Hausdorff space metrizable?

Then learn how to state the conditions carefully (specially since you

bitch so much about lack of precision in Top. Atlas )

: Can _any_/_every_ countable

compact Hausdorff space be mapped into [0,1]? I thought you meant if there

were non-trivial cases (meaning not closed intervals ) of compact Hausdorff

spaces that map continuously into [0,1].


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