data
data copied to clipboard
pi-base
A community database of topological counterexamples
As mentioned in #640 . I have checked that all manually-deduced implications are still there (perhaps now being autometic).
The space $\omega_2$ or $\omega_12$: An example of LOTS+~compact+~first countable+countably compact
(I am sorry to open up so many issues at a time, but I am afraid that I would forget if I didn't do that.) Currently there is no space...
As shown in {{mathse:4913523}} (https://math.stackexchange.com/q/4913523). On the other hand, we can be inspired by the given answer to construct an example which is LOTS and sequentially discrete but not discrete....
The property "if $X=\displaystyle\bigcup_{n\in\mathbb{N}} C_n$ with $(C_n)$ being a countable disjoint family of closed subsets, then one of $C_n$ is $X$ and the others are empty" is quite interesting. Equivalently,...
Two years ago I got from https://math.stackexchange.com/questions/4453285 that $[0,1]^\omega$ is a nontrivial example for a LOTS that is connected and totally path disconnected (such example does not exist in $\pi$-base...
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...
As I work on #130, I'm seeing a bunch of redundancy blocking efficient contributions. The decision for each property having a file was based on the assumption each property needed...
Some comments for you and Jocelyn to discuss. S154/P187: "non-trivial sequence" is not clear and seemingly not right. You probably meant a sequence of all distinct elements instead. T473: "Asserted...
@jocelynbell @StevenClontz Note that Steen & Seebach space 94 item 4 says that the space is not [P9](https://topology.pi-base.org/properties/P000009) (functionally Hausdorff). That is better than quoting the General Reference Chart to...