Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 16 (2009), No. 2, 377--390
Copyright Heldermann Verlag 2009

Subbases for N-ary Convexities

Evgeny Sharikov
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.

MSC: 52A01

[ Fulltext-pdf  (150  KB)] for subscribers only.