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Started totally convex space as a spin-off from algebraic theories in functional analysis.
Great!
I didn't edit the article nearly as much as the diff makes it look. But I had to edit the header sizes to make the TOC work, and my grammar meter made me cut out at least one word in each paragraph, so ….
Well, OK, I did a second definition.
Also, I removed the claim that the first example consists of the free TCSes, since not every Banach space is of the form .
Thanks!
I have completed the bibdata (adding author names(!), volume, page range and DOI):
Dieter Pumplün, Helmut Röhrl: Banach Spaces and totally convex spaces I, Comm. Alg. 12 8 (1984) 953-1019 [doi:10.1080/00927878408823035]
Dieter Pumplün, Helmut Röhrl, Banach Spaces and totally convex spaces II, Comm. Alg. 13 5 (1985) 1047-1113 [doi:10.1080/00927878508823205]
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