We show that a subset C of the euclidean space which agrees with the closure of its interior is convex if and only if for everyconvex body D which meets its interior it is possibleto control, in a suitable way, the distance of a point from the intersection between C and D by means of its respectivedistances from C and D.
A Metric Characterization of Convex Bodies / Benassi, Carlo 6/8/1962; M., Boni; Gavioli, Andrea. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - ELETTRONICO. - 43:(1995), pp. 101-112.
A Metric Characterization of Convex Bodies
BENASSI, Carlo 6/8/1962;GAVIOLI, Andrea
1995
Abstract
We show that a subset C of the euclidean space which agrees with the closure of its interior is convex if and only if for everyconvex body D which meets its interior it is possibleto control, in a suitable way, the distance of a point from the intersection between C and D by means of its respectivedistances from C and D.
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