Author:
Bárány Imre,Zamfirescu Tudor
Abstract
The most usual diameters in the world are those of a sphere and they all contain its centre. More generally, a chord of a convex body in Rd is called a diameter if there are two parallel supporting hyperplanes at the two endpoints of the chord.It is easily seen that there are points on at least two diameters. From a result of Kosiński [6] proved in a more general setting it follows that every convex body has a point lying on at least three diameters. Does a typical convex body behave like a sphere and contain a point on infinitely or even uncountably many diameters?But what is a typical convex body? The space 𝒦 of all convex bodies (d-dimensional compact convex sets) in Rd, equipped with the Hausdorff metric, is a Baire space.
Publisher
Canadian Mathematical Society
Cited by
9 articles.
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