Journal of Convex Analysis 16 (2009), No. 2, 377--390
Copyright Heldermann Verlag 2009
Subbases for N-ary Convexities
Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia
We introduce a notion of N-connectedness 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 N-connected.
Keywords: Axiomatic convexity, convexities of arity N, subbases for convexities and topologies.
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