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Results tagged with stone-cech-compactification
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user 150060
1
vote
2
answers
172
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Spaces $X$ with every compactification $0$-dimensional with $\beta X\setminus X$ not locally...
Previously, in this post I've shown the following characterization of spaces with only zero-dimensional compactifications:
Theorem. Let $X$ be strongly zero-dimensional and $\beta X\setminus X$ locall …
- 1,354
11
votes
2
answers
291
views
Spaces with every compactification $0$-dimensional which aren't locally compact
Recently I've proven the following theorem
Theorem. Let $X$ be a zero-dimensional locally compact Hausdorff space. Then the following are equivalent:
Every compactification of $X$ is zero-dimensional …
- 1,201
22
votes
1
answer
663
views
Are $\beta \mathbb{Q}$ and $\beta(\beta\mathbb{Q}\setminus\mathbb{Q})$ homeomorphic?
The canonical inclusion $\beta\mathbb{Q}\setminus \mathbb{Q} \hookrightarrow \beta\mathbb{Q}$ is not the Stone-Čech compactification of $\beta\mathbb{Q}\setminus \mathbb{Q}$. Even so, this doesn't nec …
- 12.9k