Can anyone provide me with an example of a compact space that has subsets that aren't compact?

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- Apr 17th 2013, 01:34 PMI-ThinkSubsets of compact spaces
Can anyone provide me with an example of a compact space that has subsets that aren't compact?

- Apr 17th 2013, 02:00 PMPlatoRe: Subsets of compact spaces
Any compact subset of a Hausdorff space with the relative topology is a compact space.

Now any open set is that compact subspace is not compact. WHY?

Example: $\displaystyle [-2,2]\subset \mathbb{R}^1$ with the relative topology is a compact space.

But $\displaystyle (0,1)$ is not compact.