Moniker1998

metrizable + realcompact => non-measurable cardinality

1

Hi I'd like to replace [theorem 394](https://topology.pi-base.org/theorems/T000394) by the stronger P53 metrizable + P162 realcompact => P164 non-measurable I don't think it exists in literature, [here's the math stackexchange link](https://math.stackexchange.com/questions/4902389/a-metrizable-space-is-realcompact-iff-it-has-non-measurable-cardinality/4902390)...

$X$ is completely uniformizable (or Dieudonne complete) if $X$ has an admissible uniform structure in which it's complete (as a uniform space) [link to definition on wikipedia](https://en.wikipedia.org/wiki/Completely_uniformizable_space) **Theorems:** P162 realcompact...

Different types of local compactness, a missing example

9

Hi, I've noticed that there is no space or theorem that would give an example or counter-example to the following. A space that's weakly locally compact, not locally compact and...

Regular extremally disconnected P-space of non-measurable size

1

Hello, since we already have all the tools for it in pi-base, I thought the following theorem would be a nice addition, which shows that modulo size, all regular extremally...

Bing's space is realcompact?

6

I think the property was very successfully introduced to pi-base. In #372 I mention ~~two spaces~~ a space in which it still needs to be verified. Those are Bing's space...

Regular non-normal extremally disconnected space

4

The space (or spaces) $\Pi$ from Gillman and Jerison is an example of Tychonoff extremally disconnected space which isn't normal. The construction is similar to Mrówka-Isbell space but the construction...

Mysior plane

17

Mysior plane, first defined by Mysior, is an example of a space that's union of two closed realcompact subspaces but which isn't realcompact. Definition can be found in [this article](https://dml.cz/handle/10338.dmlcz/142888...

A property that isn't on pi-base is that of strongly zero-dimensional spaces. Those are spaces $X$ for which the Lebesgue covering dimension or equivalently large inductive dimension is $0$. Equivalently,...

This property could be added. See [here](https://doi.org/10.2307/2036606) for reference. A space is called subparacompact if every open cover has a $\sigma$-discrete closed refinement. Alias: $\sigma$-paracompact space

Properties independent of ZFC

1

Whenever you search in the search tab a property that is impossible in ZFC, it gives you a message for it. Could the same be done with properties independent of...