Ralf Kemper

Cogenerators for Convex Spaces

We give cogenerators for the categories of convex (= finitely superconvex), finitely positively convex, and absolute convex (= finitely totally convex) spaces introduced by Pumplün and Röhrl.

Positively Convex Spaces

AbstractWe give a construction of the left adjoint of the comparison functor

Epimorphisms of absolutely convex spaces

\widehat\Delta :Ban_{\text{1}}^{\text{ + }} \to PC {\text{(resp}}{\text{. }}\widehat\Delta _{{\text{fin}}} {\text{: }}Vec_{\text{1}}^{\text{ + }} \to PC_{{\text{fin}}} {\text{)}}

Epimorphisms of separated totally convex spaces

in one step and we give a characterization of separated (finitely) positively convex spaces.

Injective and Epi-Projective Objects in Categories of Convex Spaces

We construct a cogenerator for the category of preseparated superconvex spaces, and we describe separated convex spaces, i.e. convex spaces for which the morphisms into the unit interval separates points.

Epimorphisms of Separated Superconvex Spaces

(1994). Epimorphisms of absolutely convex spaces. Communications in Algebra: Vol. 22, No. 8, pp. 3183-3195.

Normed totally convex spaces

We introduce the categories Vecp of p-normed vector spaces, Banp of p-Banach spaces, ACp of p-absolutely and TCp of p-totally convex spaces (0 < p ≤ 1). It will be shown that TCp(ACp) is the Eilenberg–Moore category of Banp(Vecp). Then congruence relations on TCp(ACp)-spaces are studied. There are many differences between TCp(ACp)-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplün and Röhrl, 1984, 1985), which will become apparent in Section 4.

Epimorphisms of Discrete Totally Convex Spaces

We give characterizations of the epimorphisms in the categories of open and separated totally convex and (pre)separated absolutely convex spaces.