Geodesic
Abstract Convexity and Connectedness
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 565-588 Cet article a éte moissonné depuis la source Heldermann Verlag

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In a former paper the concept of n-ary connectedness was introduced, where 1-ary connectedness coincides with the usual notion of (abstract) connectedness. In the present paper, sets endowed with a convexity structure are studied, where the polytopes are n-ary connected. Interrelations between the classical Helly and Carathéodory numbers are evaluated as a pre-stage of Helly and Carathéodory type intersection theorems. Various other applications such as intersection theorems and fixed point theorems for trees and hyperconvex metric spaces are presented.
Classification : 52A01, 52A30, 52A35, 54D05
Mots-clés : Connected, convex, star-shaped, selector, set-valued function 
@article{JCA_2007_14_3_JCA_2007_14_3_a5,
     author = {J. Kindler},
     title = {Abstract {Convexity} and {Connectedness}},
     journal = {Journal of convex analysis},
     pages = {565--588},
     year = {2007},
     volume = {14},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a5/}
}
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J. Kindler. Abstract Convexity and Connectedness. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 565-588. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a5/