Jianing-Song
Jianing-Song
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...
This is analogous to KC = "every compact subset is closed". Proof: Suppose that $X$ is US. Let $C$ be a sequentially compact subset of $X$, then there is no...
Removed the implications $T_i\Rightarrow T_1$ for $i=2,4,5,6$ since they are not needed. I also changed a bit the wording of T488.
Now we have $\sigma$-connected => connected and path-connected => $\sigma$-connected. Of course, the proof of path-connected => connected is much simpler than path-connected => $\sigma$-connected, so it is a question...
Please forgive me if this has already been mentioned in previous issues. MathSE has a link that mentions the proof that the Sorgenfrey line is not LOTS: https://math.stackexchange.com/questions/1603512/sorgenfrey-line-is-not-orderable. Unfortunately, this...
Hi everyone, I will be soon back from summer holiday, and I would like to add the following theorems: $\bullet$ ~empty + completely metrizable + ~has an isolated point $\Rightarrow$...