Timeline for A generalization of metric spaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 2, 2020 at 19:01 | comment | added | Gabe Conant | As long as one drops the subtraction axiom ($a<b\Leftrightarrow \exists c\, a+c=b$) then $X\cup\{0\}$ is an "algebraic structure" as in the question, but just with the binary operation of $\max$. (Btw, OP does not impose extra structure on the domain of the metric, just the codomain.) One can go further and relax totality of the order to obtain "lattice-valued" ultrametrics (e.g., as in this paper, though surely the concept is older). | |
| Jun 24, 2020 at 17:14 | comment | added | Chilote | It is more general in the sense that no algebraic structure is required in the domain nor codomain of the "metric". The price to pay is that it only generalizes ultrametric spaces. | |
| Jun 23, 2020 at 17:10 | comment | added | LSpice | Is this a strictly more general concept? The original question covers all metric spaces, whereas yours (as you point out) only obviously covers ultrametric spaces. | |
| Jun 22, 2020 at 18:40 | history | edited | Chilote | CC BY-SA 4.0 |
added 248 characters in body
|
| Jun 22, 2020 at 18:31 | history | answered | Chilote | CC BY-SA 4.0 |