Timeline for Product topology from two premetric spaces induced by sum of premetrics?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2022 at 9:15 | comment | added | Taras Banakh | @JochenWengenroth Of course, you are right about $m$. The sequentially closed subset of $M_1\times M_2$ which is not closed is the ``diagonal'' $\{(z,z): z\in M_1\setminus\{0\}\}$ of $M_1\times M_2$. | |
| Jun 2, 2022 at 9:10 | history | edited | Taras Banakh | CC BY-SA 4.0 |
added 2 characters in body
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| Jun 2, 2022 at 9:04 | comment | added | Jochen Wengenroth | The elements of $M_1$ are probably $1/n+i/mn$ with $n\in\mathbb N$ and $m\in\mathbb N$? What is a sequentially closed subset of $M_1\times M_2$ which is not closed? | |
| Jun 2, 2022 at 3:45 | comment | added | Taras Banakh | @rmcerafl Yes, I mean that the product topology on $M_1\times M_2$ can be non-sequential. If the product topology is sequential, then I do not know the answer. | |
| Jun 1, 2022 at 21:57 | comment | added | fsp-b | (Also (excuses for my naivety but I'm far from being a topologist): If you say that ''the product $M_1\times M_2$ is not sequential'' then you do mean that the product topology on $M_1\times M_2$ is not sequential, right?) | |
| Jun 1, 2022 at 21:48 | comment | added | fsp-b | Thank you, @Taras! Do you know if the question can be answered positively if the product $M_1\times M_2$ is assumed to be sequential? | |
| Jun 1, 2022 at 21:41 | vote | accept | fsp-b | ||
| Jun 1, 2022 at 20:41 | history | answered | Taras Banakh | CC BY-SA 4.0 |