Tagged Questions
4
votes
1answer
45 views
How to show this space $X$ is countably compact, first countable?
Consider the subspace $X$ of $(2^\omega)^+$, i.e., the smallest
cardinal greater then $2^\omega$, equipped with the ordered topology
consisting of all ordinals of countable cofinality.
How to ...
1
vote
2answers
77 views
Is $\omega_{\alpha}$ sequentially compact?
For an ordinal $\alpha \geq 2$, let $\omega_{\alpha}$ be as defined here.
It is easy to show that $\omega_{\alpha}$ is limit point compact, but is it sequentially compact?
10
votes
1answer
442 views
Countable compact spaces as ordinals
I heard at some point (without seeing a proof) that every countable, compact space $X$ is homeomorphic to a countable successor ordinal with the usual order topology. Is this true? Perhaps someone can ...
