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Results tagged with stone-cech-compactification
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user 61536
17
votes
Is $\beta \mathbb{N}$ homeomorphic to its own square?
The spaces $\beta \mathbb N$ and $\beta\mathbb N\times \beta\mathbb N$ are not homeomorphic.
To derive a contradiction, assume that $\beta\mathbb N$ and $\beta\mathbb N\times \beta\mathbb N$ are home …
- 41.8k
4
votes
Accepted
A question about realcompact spaces
There exists a Tychonoff space $X$ such that $\beta X\setminus X$ is countably compact but $\beta X\setminus \upsilon X$ is locally compact, $\sigma$-compact and not countably compact. Such a space ca …
- 41.8k
8
votes
Are all free ultrafilters 'the same' in some sense?
It is consistent that all ultrafilters are the same in the following sense: for any free ultrafilters $\mathcal U,\mathcal V$ on $\omega$ there exists a finite-to-one map $f:\omega\to\omega$ such that …
- 41.8k
4
votes
Accepted
A permutation group inducing a topologically transitive action without dense orbits on $\ome...
It turns out that this problem is independent of ZFC because of the following simple
Theorem. Under $\mathfrak t=\mathfrak c$, every topologically transitive continuous action of a group $G$ on $\ …
- 41.8k