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Results tagged with stone-cech-compactification
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user 61785
1
vote
Accepted
Functor from rings into compact Hausdorff spaces
Here is an answer to your question about monadicity, as it's too long for a comment. I will not fill in every detail, so if you follow along there will be several definitions that need to be expanded …
- 3,768
3
votes
Stone-Cech Compactification of the real line
The answer is no, essentially because $\mathbb{R}$ embeds as a locally compact open subspace of $\beta\mathbb{R}$, and $\mathbb{R}$ is not an F-space.
In detail, for the purposes of this answer I wi …
- 3,768
5
votes
Accepted
Borel $\sigma$-algebra in $\beta \mathbb N \times \beta \mathbb N$
The answer is no.
Jiří Nedoma proved that if $(X,\Sigma)$ is a measurable space $|X| > 2^{\aleph_0}$, then the diagonal is not a measurable subset of $(X\times X, \Sigma \otimes \Sigma)$. (The articl …
- 3,768