Euclidean Topology I: Basic Concepts
Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects

AF222 V1 Article

Euclidean Topology I: Basic Concepts
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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4. Euclidean Topology I: Basic Concepts

The third general mathematical framework is that of Euclidean topology, which involves considering Euclidean space $ℝ_{2}^{n}$ as the surrounding topological vector space.

Euclidean topology is induced by the Euclidean metric, denoted by d₂, for which $B^{n} (x, r]$ and $B^{n} (x, r]$ denote, respectively, the open ball centered at x with radius r and the closed ball centered at x with radius r (r >...

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Euclidean Topology I: Basic Concepts

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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) - BLOCH (E.D.) - A First Course...

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