8. Algebraic and topological integer dimensions
The notion of topological dimension extends that of the algebraic dimension of a vector space. It is a topological invariant, integer or infinite.
8.1 The concept of dimension
Although established earlier, the concept of whole dimensions was defined by Euclid of Alexandria in the first book of his treatise "The Elements" (ca. 300 BC). The notion of dimensions greater than three is due to R. Descartes (1637).
A dimension is represented by a functional, generically denoted dim, defined on a class of subsets of a topological space E and with values in
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Algebraic and topological integer dimensions
Dimension in Euclidean space...
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