Timeline for Metric spaces as algebraic systems
Current License: CC BY-SA 2.5
4 events
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| Dec 27, 2010 at 23:04 | comment | added | arsmath | There's a published form of a somewhat analogous presentation for Banach spaces -- totally convex spaces -- in the category theory literature, so it's a natural place to look. (It's not exactly analogous because in that case the signature includes one infinitary operation.) | |
| Dec 27, 2010 at 23:01 | comment | added | arsmath | Maybe contact Adamek? The axiomatization shows that the category of extended metric spaces with non-expansive maps is locally presentable. ("Extended", because you have to allow the metric to take on infinite values. This corresponds to pairs of points (x,y) where none of the predicates hold.) Since Ademek included this example in his category theory text, and is also an expert on local presentability, he might know if there's a published form of the result. | |
| Dec 27, 2010 at 1:08 | comment | added | user6976 | I also thought that this was standard but the problem is with a precise reference. The idea to view metric spaces as algebraic structures is useful when one wants to apply model theory (that is how it is used in [KSTT]. The idea is quite natural but the question is who invented it first. | |
| Dec 26, 2010 at 23:30 | history | answered | arsmath | CC BY-SA 2.5 |