Some conjectures in general topology

[felixpernegger]

What is the conjecture

A nice list of open 20 problems can be found in
https://www.math.md/files/basm/y2013-n2-3/y2013-n2-3-(pp37-46).pdf.pdf

As far as I can tell (by going over citations in Google scholar), so far all are still open except Problem 11, which has been solved in
https://arxiv.org/pdf/2006.12675

Like usual in set theory related topics, many of the problems are known to be true under CH or some other additional axiom. A formalisation should probably reflect that.

Problem 1 is PR #1810.

I think this would be nice to have, as right now the repository basically only contains one conjecture in topology at all (#1776).

Prerequisites needed

Most likely all problems need some sort of additional definition, but this is typically a fairly easy task.

AMS categories

• ams-54

Choose either option

• I plan on adding this conjecture to the repository
• This issue is up for grabs: I would like to see this conjecture added by somebody else

[Paul-Lez]

Very nice! I'd suggest opening sub-issues so that people can claim the problems individually (and we can track progress on this issue)

[felixpernegger]

Very nice! I'd suggest opening sub-issues so that people can claim the problems individually (and we can track progress on this issue)

I dont think I have perms to create subissues directly?

[mo271]

While we could use subissues, I'd prefer just normal issue and then we can create a milestone for the collection, like we have for Ben Green's problem for instance

[felixpernegger]

While we could use subissues, I'd prefer just normal issue and then we can create a milestone for the collection, like we have for Ben Green's problem for instance

I think a milestone sounds great! Maybe 20 problems is a bit little though?
In any case, I think milestones can bring down the current bias towards number theory and combinatorics (80.1%) a little bit, since they set clear goals to work towards.
A similar but much longer list is for example
https://staff.fnwi.uva.nl/j.vanmill/papers/papers1990/opit.pdf

[Paul-Lez]

I'll claim problems 5 - 7 (the ones in the Symmetrizable spaces section)

[felixpernegger]

I'll claim problems 5 - 7 (the ones in the Symmetrizable spaces section)

FYI I checked this before and if I remember correctly one or two of those actually have a simple counterexample

I recommed you to use the "Explore" tab of this website to check:
https://topology.pi-base.org/spaces

[mo271]

I think a milestone sounds great! Maybe 20 problems is a bit little though?

It's fine, why not a smaller Milestone for once...

A similar but much longer list is for example
https://staff.fnwi.uva.nl/j.vanmill/papers/papers1990/opit.pdf

sounds also like a good list for us!! (probably a different milestone