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p-Banach Spaces and p-Totally Convex Spaces

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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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Kemper, R. p-Banach Spaces and p-Totally Convex Spaces. Applied Categorical Structures 7, 279–295 (1999). https://doi.org/10.1023/A:1008653724200

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