Geodesic
Subbases for N-ary Convexities
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 377-39

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 52A01
Mots-clés : Axiomatic convexity, convexities of arity N, subbases for convexities and topologies 
@article{JCA_2009_16_2_JCA_2009_16_2_a3,
     author = {E. Sharikov},
     title = {Subbases for {N-ary} {Convexities}},
     journal = {Journal of convex analysis},
     pages = {377--39},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a3/}
}
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E. Sharikov. Subbases for N-ary Convexities. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 377-39. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a3/