p-Banach Spaces and p-Totally Convex Spaces |
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| Authors: | Ralf Kemper |
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| Institution: | (1) Fachbereich Mathematik, Fernuniversität, 58084 Hagen, Germany |
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| Abstract: | We introduce the categories Vec
p
of p-normed vector spaces, Ban
p
of
p
-Banach spaces, AC
p
of
p
-absolutely and TC
p
of
p
-totally convex spaces (0 < p  1). It will be shown that TC
p
(AC
p
) is the Eilenberg–Moore category of Ban
p
(Vec
p
). Then congruence relations on TC
p
(AC
p
)-spaces are studied. There are many differences between TC
p
(AC
p
)-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplün and Röhrl, 1984, 1985), which will become apparent in Section 4. |
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| Keywords: | p-Banach space p-normed vector space (p-) totally (resp (p-) absolutely) convex space congruence relation Eilenberg– Moore category monad |
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