Timeline for A spectral characterization of path connected spaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 2, 2020 at 13:07 | comment | added | Jeremy Brazas | @TarasBanakh That is the question I would ask...As stated, the question is answered. I cannot tell if the OP is satisfied or wants other cases addressed. My comment is meant to encourage the OP to revise the question. I will consider thinking about it more when I know what the revised question really is. | |
| May 2, 2020 at 7:33 | comment | added | Taras Banakh | @JeremyBrazas What about metrizable counterexamples? | |
| Apr 25, 2020 at 3:38 | comment | added | Jeremy Brazas | The one-point compactification of $\omega_1\times [0,1)$ with the order topology is indeed a counterexample. This question might be more interesting with an extra hypothesis on $X$, e.g. sequential, first countable, or metrizable. | |
| Apr 25, 2020 at 3:32 | comment | added | R. van Dobben de Bruyn | I think the extended long line $\bar L$ (add one point at each end) is a counterexample. Every map $\bar L \to \mathbf R$ (or to $\mathbf C = \mathbf R^2$) is eventually constant so the image is path connected, but $\bar L$ itself is too long to be path connected. | |
| Apr 25, 2020 at 2:52 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 10 characters in body
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| Apr 25, 2020 at 2:45 | history | asked | Ali Taghavi | CC BY-SA 4.0 |