
Journal of Convex Analysis 16 (2009), No. 2, 377390 Copyright Heldermann Verlag 2009 Subbases for Nary Convexities Evgeny Sharikov Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia e.sharikov@mail.ru We introduce a notion of Nconnectedness of a topological space with respect to a convexity on this space. For a given collection H of subsets of a set X we introduce different convexities and topologies on both H and X. Then we prove that the convexity G generated by H is of arity N whenever H is connected and X is Nconnected. Keywords: Axiomatic convexity, convexities of arity N, subbases for convexities and topologies. MSC: 52A01 [ Fulltextpdf (150 KB)] for subscribers only. 