TERMIUM Plus^®

Fiche 1,  Justifications,  Anglais

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This notion of topological dimension has been formalized in the twentieth century on the basis of the idea of Poincaré (1905, Chap. III, S3) to let a point have zero dimension, to relate the dimension of a space to the way it can be divided by boundaries, and to use mathematical induction. Thus curves can be divided by cuts which are of zero dimension (i.e. by points) and so have one dimension, surfaces can be divided by cuts of one dimension (i.e. by curves) and so have two dimensions, etc. Cantor's middle-thirds set had no place in Euclid's Elements, of course, but it may be said to have topological dimension d = O because it is a subset of R with zero length (and so has neither breadth nor length).  2, fiche 1, Anglais, - topological%20dimension

Fiche 1,  Justifications,  Français

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Ensemble dont la dimension fractale est égale ou supérieure à sa dimension ordinaire (topologique).  2, fiche 1, Français, - dimension%20topologique

Fiche 1,  Justifications,  Espagnol