Abstract convexity, some relations and applications

Juan Vicente Llinares

CEPREMAP Working Papers (Couverture Orange) from CEPREMAP

Abstract: The aim of this paper is to analyze the relationship between different notions of abstract convexity structures that we can find in the literature in connection with the problem of the existence of continuous selections and fixed points to correspondences. Mainly we will focus in the notion of mc-spaces, which was introduced in LLinares (1994, 1997), and its relationship with c-spaces (Horvath, 1991), simplicial convexity (Bielawski, 1987) an order convexity (used in Horvath and LLinares, 1996), B'-simplicial convexity and L-spaces (Ben-El-Mechaiekh and al., 1997). Moreover, in the context of mc-spaces, a characterization result of non-empty finite intersection in the line of the Knaster-Kuratowski-Mazurkievicz lemma, some consequences of it and some generalizations of Browder's existence of continuous selection and fixed point theorem are presented.

Date: 1998

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Persistent link: http://EconPapers.repec.org/RePEc:cpm:cepmap:9803

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