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Results tagged with stone-cech-compactification
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user 6794
3
votes
When are the zero sets of two continuous functions in the Stone-Čech compactification includ...
I'm reasonably convinced (but don't have time to check it carefully right now) that $Z(f^\beta)\subseteq Z(g^\beta)$ if and only if, for every $\varepsilon>0$, $f$ is bounded away from zero on $\{x\i …
- 73.1k
10
votes
The need for nets in topology
There seems to be a gap in your argument where, under the assumption that the system of neighborhoods could be totally ordered, you seem to use that this total order must be countable. To fill the ga …
- 73.1k
9
votes
Accepted
Addition and Rudin-Keisler ordering in $\beta \omega$
For Question 1: First, there are idempotent ultrafilters, so some ultrafilters satisfy 1 in a very strong form. But 1 does not hold in general. The reason is that the semigroup $\beta\omega-\omega$ ha …
- 73.1k