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




Re: Onto [0,1]
Posted:
Apr 21, 2013 4:40 AM


On Apr 21, 2:56 am, William Elliot <ma...@panix.com> wrote: > Can an uncountable compact Hausdorff be continuously mapped onto [0,1]?
Let X be the ordinal omega_1 + 1 with its order topology. X is an uncountable compact Hausdorff space. X can not be continuously mapped onto [0,1]. (Hint: X is scattered.) Whether X can be discontinuously mapped onto [0,1] is independent of ZFC.



