Timeline for What is the "right" universal property of the completion of a metric space?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2010 at 6:22 | comment | added | Harrison Brown | For reference: It's in <i>CftWM</i>, pp. 56-57 in my edition (which agrees with Google Books!) It doesn't seem to be discussed much beyond that. | |
| Jan 13, 2010 at 5:03 | comment | added | Mariano Suárez-Álvarez | Yes, but only taking isometric embeddings results in a weaker universal property. One could ask: if $\mathbf{Met}$ is the category of metric spaces and continuous maps, what subcategories $\mathbf{Met}'$ of $\mathbf{Met}$ containing all objects have the property that their full subcategory spanned by the objects which are complete is reflective? | |
| Jan 13, 2010 at 4:40 | comment | added | Pete L. Clark | OK, I can see that I will have to have a look at Mac Lane's book (I assume you mean Categories For the Working Mathematician). But isn't everything you said true with "uniformly continuous map" replaced by "isometric embedding"? | |
| Jan 13, 2010 at 4:26 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 2.5 |