Geodesic
Lines and Hyperplanes associated with Families of Closed and Bounded Sets in Conjugate Banach Spaces
Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 933-938

Voir la notice de l'article provenant de la source Cambridge University Press

Let be a family of sets in a linear space X. A hyperplane π is called a k-secant of if π intersects exactly k members of . The existence of k-secants for families of compact sets in linear topological spaces has been discussed in a number of recent papers (cf. [3–7]). For X normed (and a finite family of two or more disjoint non-empty compact sets) it was proved [5] that if the union of all members of is an infinite set which is not contained in any straight line of X, then has a 2-secant. This result and related ones concerning intersections of members of by straight lines have since been extended in [4] to the more general setting of a Hausdorff locally convex space. 
Edelstein, M. Lines and Hyperplanes associated with Families of Closed and Bounded Sets in Conjugate Banach Spaces. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 933-938. doi: 10.4153/CJM-1970-107-3
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