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Results tagged with stone-cech-compactification
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user 17064
3
votes
1
answer
152
views
Stone-Čech compactification of a Boolean subalgebra of $\{0,1\}^S$
Setup: Let $S$ be a set. Let $B$ be a Boolean subalgebra of $\{0,1\}^S$; i.e., just to be clear $B$ contains the constant $0$ and $1$ functions, and is stable under binary pointwise $\land$, $\lor$ a …
- 32.5k
7
votes
1
answer
317
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Ultrafilters of closed sets
The following definition should be standard, but let me state it just in case there is some ambiguity:
If $\mathscr{L}$ is a set of subsets of a set $X$ that is closed under finite unions and intersec …
- 5,596
8
votes
2
answers
397
views
When are the zero sets of two continuous functions in the Stone-Čech compactification includ...
Let $X$ be a topological space (feel free to add some simplifying assumptions here, like “completely regular” provided at least the case of finite-dimensional manifolds is covered). Let $f,g \in C^*( …
6
votes
1
answer
412
views
Tychonoff-ization and Urysohn (functionally Hausdorff) topological spaces
Let me first make sure I have the correct definitions because my question will be about the difference about the two and there may be some massive confusion on my part.
A topological space $X$ is sai …
- 11.4k
6
votes
1
answer
475
views
Is the absolute of a compact space the projective limit of the Stone-Čech compactifications ...
Is the following statement true, and if it is, does someone have a reference?
Let $X$ be a compact (i.e., compact and Hausdorff) topological space. Then the Gleason space (=Iliadis absolute, =Sto …
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