Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Second countable
Replies: 2   Last Post: Feb 13, 2013 6:13 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Kaba

Posts: 289
Registered: 5/23/11
Second countable
Posted: Feb 13, 2013 4:55 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
sigma-compact, but let's concentrate on this implication. I've managed
to prove X Lindelöf and first-countable, 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


Date Subject Author
2/13/13
Read Second countable
Kaba
2/13/13
Read Re: Second countable
quasi
2/13/13
Read Re: Second countable
Kaba

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.