Euclidean Topology II: Curves and Surfaces
Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects

AF222 V1 Article

Euclidean Topology II: Curves and Surfaces
Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects

Author : Jean-Charles PINOLI

Publication date: May 10, 2026 | Lire en français

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5. Euclidean Topology II: Curves and Surfaces

5.1 Curves

Simply put, a curve is a subset of points in Euclidean space $ℝ_{2}^{2}$ or $ℝ_{2}^{3}$ (and more generally $ℝ_{2}^{n}$ ) on which it is possible to locate oneself locally using a single real coordinate, or a path along which a point moves continuously. It resembles a line segment that is continuously deformed. A curve in $ℝ_{2}^{2}$ ...

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Euclidean Topology II: Curves and Surfaces

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Convex Geometry

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).
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