I'm looking for two examples:
- A space which is compact but not sequentially compact
- A space which is sequentially compact but not compact
Explanations why the spaces are compact / not compact and sequentially compact / not sequentially compact would be appreciated. A reference would also be appreciated. So the conclusion would be, that there's no equivalence in general. Of course they are equivalent in a metric space.
math
Best Answer
The following examples are from $\pi$-Base, a searchable database of Steen and Seebach's Counterexamples in Topology.
(Click on the following links to learn more about the spaces.)
For compact but not sequentially compact:
For sequentially compact but not compact: