Timeline for Quotient of compact metrizable space in Hausdorff space
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2018 at 12:08 | comment | added | VMrcel | Oh you are right, I'll think about it, thank you ! | |
| Jun 25, 2018 at 10:53 | comment | added | Taras Banakh | @VMrcel You can extend the Cantor starcase function to a continuous function on the closed interval and then you will get a continuous function between closed intervals, for which the quotient pseudometric still is zero. By the way, the quotient space is path-connected in the quotient metric (since it determines the anti-discrete topology). So, maybe some more precise question should be asked (but a good question is a half of an answer). | |
| Jun 25, 2018 at 9:44 | comment | added | VMrcel | Thank for the answer ! Indeed it is the same counter-example than in the question I have quoted. However, I have realised that I need to deal with path-connected spaces so that quotient space is path-connected in the quotient pseudo-metric. Is there a known example that does not use the cantor set ? | |
| Jun 20, 2018 at 15:48 | history | edited | Taras Banakh | CC BY-SA 4.0 |
added 216 characters in body
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| Jun 20, 2018 at 15:39 | history | answered | Taras Banakh | CC BY-SA 4.0 |