## New answers tagged stone-cech-compactification

4
votes

Accepted

### Points in the Stone Cech compactification are intersection of open sets

Yes if the point is from $\mathbb{N}$ (it is isolated).
No if the point is in $\beta\mathbb{N}\setminus\mathbb{N}$ because in that subspace every nonempty $G_\delta$-set has nonempty interior, see ...

5
votes

### Elementary equivalence between $n\mapsto n+1$ and its inverse on the Stone-Čech remainder?

Yes, these two structures are elementarily equivalent.
This is proved as a corollary to another theorem, which states
Theorem: CH implies that $\Phi$ and $\Phi^{-1}$ are conjugate to each other in the ...

2
votes

### Near permutation $n\mapsto n+1$ not conjugate to its inverse on the Stone-Čech remainder?

The question is answered by Will Brian arXiv, Feb. 6 2024.

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