Convex Geometry
Geometry of Euclidean Sets I: Vector, Topological, and Metric Aspects

Article REF: AF222 V1

Convex Geometry
Geometry of Euclidean Sets I: Vector, Topological, and Metric Aspects

Author : Jean-Charles PINOLI

Publication date: May 10, 2026 | Lire en français

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6. Convex Geometry

The fourth general mathematical framework is that of convex geometry, which is the branch of geometry that deals with convex sets and, more generally, star sets in vector spaces.

6.1 Convex sets

Definition (convex subset). A nonempty subset X of $ℝ_{2}^{n}$ is convex (convex set) if it contains all the closed line segments connecting each pair of points in the set; in other words:

\forall x, y \in X, [x, y] \subseteq X,

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Bibliography

(1) - AUBIN (J.P.), FRANKOWSKA (H.) - Set-Valued Analysis, - Birkhäuser (1990).
(2) - BERGER (M.) - Geometry, - Springer, vol. 1 and 2, [1st ed., 1987] (2009).
(3)...

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