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. I am guessing the example will be an exotic function space.