3
$\begingroup$

I would like to know how is it going the research in compactifications of locally compact Hausdorff spaces. Are there people doing this? Are there relevant conjectures on it?

$\endgroup$

1 Answer 1

2
$\begingroup$

I would not think it is particularly active, unless you are prepared to add more structure, for instance, study wonderful compactifications:

https://en.wikipedia.org/wiki/Wonderful_compactification

Having said that, I can recall a couple of open problems from Arkhangelski-Tkachenko's Topological Groups. I am not sure about their current status (the book is 2008). Let $X$ be Tychonoff space.

  1. When is the Cech-Stone compactification $c(X)$ a Moscow space?
  2. When does $X$ admit a Hausdorff Moscow compactification?
$\endgroup$
1
  • $\begingroup$ Thank you. Actually, I already work with compactifications of spaces with more structure. I would like to know something that is purely topological like the two problems you've said. $\endgroup$ Jul 15, 2019 at 16:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.