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user 5903
8
votes
Accepted
Reference: If $X$ is metrizable, then $X$ is realcompact iff $|X|$ is non-measurable
You can consult Problem 8.5.13 in Engelking's General Topology. It deals with Dieudonné complete spaces (Tychonoff spaces that have a complete uniformity).
Part (d) shows that every paracompact space …
- 11.4k
4
votes
Accepted
Copy of $P(\omega)/\mathrm{fin}$ on $\omega_1$
To expand my comment into an answer: take, for each $n\in\omega$, a uniform ultrafilter $u_n$ on $\omega_1$ that contains the set $\{\lambda+n:\lambda$ is a limit or $0\}$.
The set $U=\{u_n:n\in\omega …
- 11.4k