Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Evgeny Sharikov

Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia

e.sharikov@mail.ru

Keywords

  • Axiomatic convexity
  • convexities of arity N
  • subbases for convexities and topologies

Mathematics Subject Classification

52A01

Suggested citation

E. Sharikov. “Subbases for N-ary Convexities.” Journal of Convex Analysis 16 (2009), No. 2, 377–390.

Copyright Banach Press 2009