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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 ...
KP Hart's user avatar
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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 ...
Will Brian's user avatar
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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.
Mohammad Golshani's user avatar

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