Hausdorff-compact space
The notion of compactness becomes especially useful when the space is also Hausdorff. The below definition is only tagged as such so that proof graphs display correctly.
A topological space
will be called Hausdorff-compact if it is both Hausdorff and compact. topology
Properties
- Subsets are closed iff they are compact, which follows from:
- No finer compact, no coarser Hausdorff than a Hausdorff-compact
- Hausdorff-compact implies normal