Timeline for Why the name `Lipschitz-Free Banach spaces'?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2020 at 1:42 | comment | added | Yemon Choi | @user131781 Thank you for making precise what I was alluding to (I typed the original comment in a rush). Yes, G+K's paper, and some talks by G that I happened to attend, made it clear that the "freeness" property they had in mind was what the more category-theoretic inclined would call: left adjoint to the forgetful functor between the two categories described in your comment. | |
| Jun 26, 2020 at 17:31 | comment | added | Robert Furber | @user131781 Undoubtedly Yemon Choi was mimicking the OPs misspelling, the standard is "sloppiness" ("slopiness" is a conceivable way of referring to the quality of being sloped). I think you are right that it is "free" in the sense of left adjoint. Of course, $\ell^1(X)$ is the left adjoint to the forgetful closed unit ball functor to $\mathbf{Set}$, so some extra thing is needed to specify that it is not this forgetful functor that is meant, but the one to the category with Lipschitz maps, as you mentioned. | |
| Jun 26, 2020 at 17:16 | comment | added | user131781 | Add the phrase “with radius at most 1” above after “pointed metric space”. | |
| Jun 26, 2020 at 17:07 | comment | added | user131781 | I suppose that this is the standard use of “free” as in free group, free topological group, free vector space, free locally convex space, etc. The technical definition is that it can be regarded as a functor which is adjoint to a forgetful one. In this case, the one from the category of Banach spaces to that of pointed metric spaces (both with the condition that the morphisms are contractive) where one maps the Banach space to its unit ball and forgets the linear structure. By the way do you mean “slopiness” or “sloppiness”? | |
| S Jun 26, 2020 at 13:48 | history | suggested | RobPratt | CC BY-SA 4.0 |
corrected spelling in title
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| Jun 26, 2020 at 13:39 | review | Suggested edits | |||
| S Jun 26, 2020 at 13:48 | |||||
| Jun 26, 2020 at 12:09 | comment | added | Yemon Choi | I think 'slopiness' is a bit harsh. Godefroy and Kalton presumably wished to say: free with respect to Lipschitz maps. I think they were the originators of the terminology "Lipschitz-free spaces" and some later authors have followed them; every time the terminology gets repeated, there is less incentive to change it :-/ | |
| Jun 26, 2020 at 12:05 | comment | added | Ben McKay | After Isaiah Berlin, are these spaces free from Lipschitz, or free to Lipschitz? | |
| Jun 26, 2020 at 11:56 | review | First posts | |||
| Jun 26, 2020 at 12:46 | |||||
| Jun 26, 2020 at 11:54 | history | asked | A_curious_asker | CC BY-SA 4.0 |