Timeline for Quotients in categories of metric spaces
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 21 at 13:18 | vote | accept | Jochen Wengenroth | ||
| Mar 21 at 13:18 | comment | added | Jochen Wengenroth | This is even more impressive, now. However, if one only wants the example of Smirnov's deleted line $(\mathbb R,\sigma)$, it is quite elementary to check (just an $\varepsilon/2$-argument) that any $\sigma$-continuous function with values in a metric space is already continuous for the usual topology on $\mathbb R$. This shows that cr$(X_T)$ has the standard topology of the line. | |
| Mar 21 at 12:31 | comment | added | Tyrone | @JochenWengenroth Thanks for pointing out the oversight! I added an assumption to correct it. Your suggestion of using Smirnov's deleted sequence topology seems to be quite fruitful. | |
| Mar 21 at 12:29 | history | edited | Tyrone | CC BY-SA 4.0 |
Fixed stuff.
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| Mar 20 at 14:23 | comment | added | Jochen Wengenroth | One would not need the (for me) dubious argument if one could calculate cr$(X)$ explicitely for one of the six exaples provided by $\pi$-base. For Smirnov's deleted sequence topology (aka $K$-topology) on $\mathbb R$, is cr$(X)$ just the usual topology of the line? | |
| Mar 20 at 13:51 | comment | added | Jochen Wengenroth | Very impressive! There is however one step that I don't understand. You claim that $X_M$ is second countable because the finer topology of $X_T$ is second countable. This does not seem to be a valid argument: math.stackexchange.com/questions/391428 | |
| Mar 20 at 13:17 | history | edited | Tyrone | CC BY-SA 4.0 |
added 221 characters in body
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| Mar 19 at 19:17 | history | edited | Tyrone | CC BY-SA 4.0 |
edited body
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| Mar 19 at 19:14 | history | edited | Michael Hardy | CC BY-SA 4.0 |
proper MathJax usage
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| Mar 19 at 19:05 | history | answered | Tyrone | CC BY-SA 4.0 |