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Results tagged with stone-cech-compactification
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user 150060
7
votes
Accepted
Are $\beta \mathbb{Q}$ and $\beta(\beta\mathbb{Q}\setminus\mathbb{Q})$ homeomorphic?
Let me summarize the discussion in the comments as an answer. Let $\chi(x, Y)$ be the character of $x$ in $Y$ i.e. the least cardinality of a local basis of the point $x$ in space $Y$.
Proposition 1. …
- 1,201
3
votes
Spaces $X$ with every compactification $0$-dimensional with $\beta X\setminus X$ not locally...
Let $X = \beta X_0 \setminus A$ where $A\subseteq \beta X_0\setminus X_0$ and $\overline{A}\setminus A$ is locally compact, $X_0$ is strongly zero-dimensional, $A$ is scattered or countable, $A\to B$ …
- 1,201
3
votes
Spaces with every compactification $0$-dimensional which aren't locally compact
This is based on Anonymous answer.
Theorem. Let $X_0$ be a strongly zero-dimensional Tychonoff space, $Y\subseteq \beta X_0\setminus X_0$ a locally compact scattered space. Then $X = \beta X_0\setminu …
- 1,201