Timeline for Does there exist a non-hemicompact regular space for which the 2nd player in the $K$-Rothberger game has a winning Markov strategy?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2023 at 2:16 | vote | accept | Steven Clontz | ||
| Jul 11, 2023 at 22:12 | comment | added | Steven Clontz | I think T1 is necessary to use Theorem 39 in order to get the open neighborhood of a compact missing a point, see my answer. | |
| Jul 11, 2023 at 17:58 | comment | added | Steven Clontz | Well once I understand the K-Menger game argument, I guess they're all equivalent with just regular. hemicompact=>P2 has Markov winning in K-Rothberger game=>P2 has Markov winning in K-Menger game are all immediate. | |
| Jul 11, 2023 at 16:31 | history | edited | C. Caruvana | CC BY-SA 4.0 |
Addressed issues regarding T1 assumptions
|
| Jul 11, 2023 at 14:41 | comment | added | C. Caruvana | Thanks for pointing that out as I was totally ignoring regular and not $T_1$. I suspect the argument for the claim doesn't require $T_1$ even though the paper was written under an umbrella assumption that all spaces are $T_2$. I'll work on clearing this point up as soon as possible. | |
| Jul 11, 2023 at 14:27 | history | edited | C. Caruvana | CC BY-SA 4.0 |
clarified some separation axiom requirements
|
| Jul 11, 2023 at 13:42 | comment | added | Steven Clontz | I believe theorem 39 requires T1, so we have equivalence of both these Markov strategic properties and hemicompactness assuming T3. | |
| Jul 11, 2023 at 3:55 | history | edited | C. Caruvana | CC BY-SA 4.0 |
fixed typo
|
| Jul 11, 2023 at 3:51 | comment | added | C. Caruvana | Oh, right, along with the methods of duality. I'll update my answer to reflect this. | |
| Jul 11, 2023 at 3:43 | comment | added | Steven Clontz | Would thm39 of arxiv.org/pdf/1812.06379.pdf do the trick directly? | |
| Jul 11, 2023 at 3:26 | history | answered | C. Caruvana | CC BY-SA 4.0 |