Dimension Theory I: Vector Dimension and Topological Dimension
Geometry of Euclidean Sets I: Vector, Topological, and Metric Aspects
Article REF: AF222 V1
Dimension Theory I: Vector Dimension and Topological Dimension
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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9. Dimension Theory I: Vector Dimension and Topological Dimension

The seventh general mathematical framework is that of dimension theory, which is an interdisciplinary branch of mathematics related in particular to linear algebra and general topology.

9.1 Dimension of a vector space

The dimension of a vector space, or Hamel dimension, is the cardinality common to all its vector bases (i.e., the number of vectors in each of these bases, or the number of coordinates needed to specify any vector).

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9.2 Dimension of a topological space

Definition...

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