Timeline for Quotient of metric spaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2020 at 10:00 | comment | added | Robert Frost | @burtonpeterj for any metric $d$, $\lambda d$ is a metric too, right, for any arbitrary positive real $\lambda$? | |
| Feb 5, 2015 at 20:58 | comment | added | burtonpeterj | We can find such a $\lambda$ only if the quotient map is Lipschitz. So why can we assume the quotient map is Lipschitz? | |
| Feb 5, 2015 at 11:33 | comment | added | user2173168 | For example, consider a compact space $X$, $X$ has a metric $d$, $d$ therefore has an upper bound. $X/\sim$ is metrizable, it can be endowed with a metric $d'$. It is trivial to prove, there is a $\lambda>0$, such that $\lambda d'$ is smaller than $d$. | |
| Feb 5, 2015 at 11:27 | comment | added | user2173168 | because when the metric $d$ has an upper bound, you can take $\lambda d$ to make the metric arbitrarily small. | |
| Feb 4, 2015 at 17:16 | comment | added | burtonpeterj | Why is this trivially true when the metric has an upper bound? | |
| Feb 4, 2015 at 7:57 | history | edited | user2173168 | CC BY-SA 3.0 |
added 1 character in body
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| Feb 4, 2015 at 7:42 | history | answered | user2173168 | CC BY-SA 3.0 |