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Results tagged with stone-cech-compactification
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user 5690
3
votes
Non-trivial convergent sequence in Stone-Čech compactification of $\mathbb{N}$
The Stone-Čech compactification is compatible with finite disjoint unions: $\beta(A\sqcup B)=\beta A\sqcup \beta B$.
If $X=(x_n)_{n\in\mathbb N}$ were a convergent sequence with limit $x\in\beta\math …
- 43.2k
5
votes
Accepted
Non-idempotent ultrafilters in the Stone-Cech compactification
Let $\Gamma=\mathbb Z$, and consider the sequence of all odd numbers, viewed as a filter. Pick an ultrafilter containing this filter. Then this ultrafilter is not idempotent.
The reason is simple: od …
- 43.2k