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Bacle H
Posts:
283
Registered:
4/8/12


Re: Onto [0,1]
Posted:
Apr 21, 2013 11:07 PM


On Sunday, April 21, 2013 6:13:15 PM UTC7, William Elliot wrote: > On Sun, 21 Apr 2013, bacll.com wrote: > > > On Sunday, April 21, 2013 12:56:53 AM UTC7, 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 nontrivial cases (meaning not closed intervals ) of compact Hausdorff
spaces that map continuously into [0,1].
that



