Timeline for Point of continuity of separately continuous functions
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2020 at 15:07 | vote | accept | Gergo Kiss | ||
| Nov 26, 2020 at 15:05 | vote | accept | Gergo Kiss | ||
| Nov 26, 2020 at 15:07 | |||||
| Nov 18, 2020 at 0:03 | answer | added | Taras Banakh | timeline score: 4 | |
| Nov 17, 2020 at 23:38 | comment | added | Alessandro Codenotti | Also you might be interested in Namioka's paper "Separate continuity and joint continuity" | |
| Nov 17, 2020 at 23:25 | comment | added | Alessandro Codenotti | You probably know this already, but there are no counterexamples with metrizable $X$ and $Y$ | |
| Nov 16, 2020 at 17:15 | comment | added | Jochen Glueck | Concering the questions itself: This sounds rather strong to me. There's a famous theorem of Ellis which says that if $(G,\circ)$ is a group, $G$ is endowed with a compact Hausdorff topology and $\circ$ is separately continuous, then $\circ$ is automatically jointly continuous. The assertion in your question would immediately yield Ellis' theorem as a special case (by using the observation from my previous comment). | |
| Nov 16, 2020 at 17:14 | comment | added | Jochen Glueck | @DieterKadelka: I think it's worthwhile to point out that if it is true for real-valued functions, then it is also true for all functions with values in completely regular (Hausdorff) spaces (since closed sets and points in such spaces can be separated by continuous real-valued functions). | |
| Nov 16, 2020 at 15:59 | history | edited | Gergo Kiss | CC BY-SA 4.0 |
added 12 characters in body
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| Nov 16, 2020 at 15:59 | comment | added | Gergo Kiss | Yes. Thank you for the question. Real or complex valued. I modify the text accordingly. | |
| Nov 16, 2020 at 12:22 | comment | added | Dieter Kadelka | Real valued function? | |
| Nov 16, 2020 at 11:28 | review | First posts | |||
| Nov 16, 2020 at 19:33 | |||||
| Nov 16, 2020 at 11:18 | history | asked | Gergo Kiss | CC BY-SA 4.0 |