Timeline for Lifts across covering maps
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2017 at 3:23 | comment | added | Jeremy Brazas | A necessary and sufficient condition for $ev$ being quotient is given in Lemma 6.2 of tac.mta.ca/tac/volumes/30/35/30-35.pdf | |
| Aug 13, 2016 at 4:43 | history | edited | Jeremy Brazas | CC BY-SA 3.0 |
Fixed notation to match OP's
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| Aug 13, 2016 at 4:18 | comment | added | Jeffrey Rolland | @JeremyBrazas Can you edit the above? \tilde{f}: X to Z,\ and f_*(X, x_0) \subseteq p_*(Z, z_0) I think are what you meant. | |
| May 13, 2014 at 12:26 | comment | added | Jeremy Brazas | It turns out that this property of $Z$ does not depend on the choice of basepoint $z_0$ and it's a straightforward exercise to show that it implies $ev$ is quotient. | |
| May 13, 2014 at 12:25 | comment | added | Jeremy Brazas | I used a sufficient condition in that paper which is a little easier to check (I have called it wep-connectedness in a few papers for a space having enough "well ended paths"). A path $\alpha:[0,1]\to X$ is well-targeted if for every neighborhood $U$ of $\alpha$ (in the compact-open topology of $(PZ)_{z_0}$), there is an open neighborhood $V$ of $\alpha(1)$ such that for every $v\in V$, there is a path $\beta\in U$ with $\beta(1)=v$. Now $Z$ is wep-connected iff for any point $z\in Z$ there is some well-targeted path $\alpha$ from $z_0$ to $z$. | |
| May 13, 2014 at 12:09 | comment | added | William of Baskerville | This is basically what I was looking for, thank you. One more question. Are there any sufficient conditions for the map $ev$ to be quotient? | |
| May 13, 2014 at 11:55 | vote | accept | William of Baskerville | ||
| May 12, 2014 at 0:01 | history | edited | Jeremy Brazas | CC BY-SA 3.0 |
deleted 33 characters in body
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| May 11, 2014 at 23:53 | history | edited | Jeremy Brazas | CC BY-SA 3.0 |
added 205 characters in body
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| May 11, 2014 at 22:58 | history | answered | Jeremy Brazas | CC BY-SA 3.0 |