Abstract
A subset S of X is called convex if the segment [x,y] (cf. 3.C) is contained in S for every x, y ∈ S. A weaker condition is that defining star-shaped sets: S is star-shaped with center a ∈ X if [a, x] c S for every x ∈ S. In R convex sets are the same as intervals.
We’ll be working in a real affine space X of real dimension d.
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© 1984 Marcel Berger
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Berger, M., Pansu, P., Berry, JP., Saint-Raymond, X. (1984). Convex Sets. In: Problems in Geometry. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1836-2_11
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DOI: https://doi.org/10.1007/978-1-4757-1836-2_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2822-1
Online ISBN: 978-1-4757-1836-2
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