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Kaba
Posts:
289
Registered:
5/23/11


Second countable
Posted:
Feb 13, 2013 4:55 PM


Hi,
Let X be a locally Euclidean Hausdorff space. Show that if X is compact, then X is second countable.
The claim can be generalized to if and only if by replacing compact with sigmacompact, but let's concentrate on this implication. I've managed to prove X Lindelöf and firstcountable, but these seem to be too weak properties to prove second countability. I'm pretty sure that I should somehow pull in the second countable basis of R^n by the locally Euclidean homeomorphisms. Any hints?
 http://kaba.hilvi.org



