Countably compact hereditarily Lindelof spaces are sequentially compact

[Moniker1998]

No description provided.

[prabau]

Again, there is no need to mention here these more general results having to do with the tower number, etc. This is all very interesting, but the purpose of the pi-base theorem is to provide a direct proof of the result if possible, and not to "teach" about other things. Any interested user who will follow up on the result can investigate on their own.

(And maybe in the future, if we add more notions involving tower number for example, that will be the time to add results about that.)

[prabau]

The reference {{zb:1126.54010}} does not contain a link to the paper. What we do in that case is to add a direct link to the pdf (https://topology.nipissingu.ca/tp/reprints/v29/tp29201.pdf) in the text itself in parentheses after {{zb:}}.

See for example how it was done for https://topology.pi-base.org/theorems/T000507
or maybe as in https://topology.pi-base.org/spaces/S000143.

[Moniker1998]

Again, there is no need to mention here these more general results having to do with the tower number, etc. This is all very interesting, but the purpose of the pi-base theorem is to provide a direct proof of the result if possible, and not to "teach" about other things. Any interested user who will follow up on the result can investigate on their own.

(And maybe in the future, if we add more notions involving tower number for example, that will be the time to add results about that.)

Is there a reason to not mention them?

Also if there's no incentive to teach people then I have no idea why were some ideas of the past made in this community. For example keeping traits for $\mathbb{R}$ and some decisions about theorems.

[felixpernegger]

Again, there is no need to mention here these more general results having to do with the tower number, etc. This is all very interesting, but the purpose of the pi-base theorem is to provide a direct proof of the result if possible, and not to "teach" about other things. Any interested user who will follow up on the result can investigate on their own.

(And maybe in the future, if we add more notions involving tower number for example, that will be the time to add results about that.)

I also think, that if say a generalisation is more than an entire paragraph or something, it's likely not suitable, but in this case it is just one additional sentence, so why not add it.

[prabau]

Adding this sentence is cluttering things. The justifications of theorems in pi-base are meant to be short and to the point, without extraneous information that is not necessary for the proof.

Users of pi-base that are interested to know why a theorem is true will find for example a reference to a paper or a reference to a mathse post. When they look up the result in the paper, they will find related information and they can dig deeper to get a better understanding of more results. But there is no need to directly put this information in pi-base if it does not help for the proof of the first result.

Pi-base is a great reference tool that people can use to complement their learning about topology. It is not meant specifically to "teach", but learning about topology occurs as a side effect of using pi-base.

Does that make sense?

[yhx-12243]

My opinion is, 𝔱 is not very common and is only known for bleeding-edge researcher, so it is not much valuable for a normal pi-base user.

[Moniker1998]

Adding this sentence is cluttering things. The justifications of theorems in pi-base are meant to be short and to the point, without extraneous information that is not necessary for the proof.
Users of pi-base that are interested to know why a theorem is true will find for example a reference to a paper or a reference to a mathse post. When they look up the result in the paper, they will find related information and they can dig deeper to get a better understanding of more results. But there is no need to directly put this information in pi-base if it does not help for the proof of the first result.

But corollary 2.2 is a corollary to theorem 2.1 so I'm not sure what you're saying. It seems to match your criteria

[Moniker1998]

I've updated to suit your tastes

[prabau]

I am trying to make sense of the proof of thm 2.1 and I am having difficulties when the space is not T1.
The proof seems a little sloppy when there are accumulation points that are not $\omega$-accumulation points. Possibly I am missing something. Will think more and put more details here tomorrow.

[Moniker1998]

@prabau not sure what you mean. To me the proof works for any topological space