Convexity theories. IV: Klein-Hilbert parts in convex modules (Q1890941)

The Klein-Hilbert part relation is introduced over a convex module, and some results, involving especially their associate Klein-Hilbert and respectively Harnack metric, are given. [See also part 0: Foundations, the second author, ibid. 2, No. 1, 13-43 (1994; Zbl 0815.52001), part I: \(\gamma\)-convex spaces, the second author, Constantin Carathéodory: an internat. tribute. Vol. II, 1175- 1209 (1991; Zbl 0759.52002), part II: The Hahn-Banach theorem for real convexity theories, the authors, Res. Cexpo. Math. 18, 387-395 (1991; Zbl 0781.46018), part III: Classification of certain real convexity theories, the second author, Geom. Dedicata 45, No. 3, 323-340 (1993)].