Here is the background material from which I am working:
- The Cantor set is an uncountable compact Hausdorff space with empty interior.
- In a locally compact Hausdorff space, each countable set has empty interior.
- The rational numbers with the subspace topology is a non-locally compact Hausdorff space in which all compact sets have empty interior.
I am trying to find a non-locally compact Hausdorff space in which all infinite compact sets have nonempty interior, under the assumption that the space does have at least one infinite compact set. I am guessing the example will be an exotic function space.
I first posed this question without specifying that there should be at least one infinite compact set, and this was solved by Stefan H. on this site.