# Examples of non-compact space with infinite subset

• Jan 16th 2010, 05:32 PM
SamBourne
Examples of non-compact space with infinite subset
Could someone give an example of
a) a non-compact space with an infinite subset which has a limit point
b) A non-compact space with an infinite subset which has a no limit point
• Jan 17th 2010, 05:27 AM
tonio
Quote:

Originally Posted by SamBourne
Could someone give an example of
a) a non-compact space with an infinite subset which has a limit point

With the euclidean topology inherited from $\mathbb{R}$ , the set $[0,1)$ and the set $\left\{\frac{1}{n}\right\}$

b) A non-compact space with an infinite subset which has a no limit point

Do a very, VERY slight modification to the above example...(Cool)
Tonio

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• Jan 17th 2010, 11:44 AM
SamBourne
Thanks for your help, much appreciated