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HAUSDORFF DIMENSION [1 record]
Record 1 - internal organization data 2000-08-29
Record 1, English
Record 1, Subject field(s)
- Mathematics
- Computer Graphics
Record 1, Main entry term, English
- Hausdorff dimension
1, record 1, English, Hausdorff%20dimension
correct
Record 1, Abbreviations, English
Record 1, Synonyms, English
- Hausdorff Besicovitch dimension 2, record 1, English, Hausdorff%20Besicovitch%20dimension
correct
- Hausdorff-Besicovitch dimension 3, record 1, English, Hausdorff%2DBesicovitch%20dimension
correct
Record 1, Textual support, English
Record number: 1, Textual support number: 1 CONT
The Hausdorff dimension, also called the Hausdorff-Besicovitch dimension in one of the possible dimensions. 4, record 1, English, - Hausdorff%20dimension
Record number: 1, Textual support number: 2 CONT
The Hausdorff dimension is defined for any subset of R [exponent]n that you can probably imagine. This includes all open sets, closed sets, countable unions of closed sets, countable intersections of open sets, etc. It will follow easily from the definition that Hausdorff dimension is not invariant under homeomorphisms. However, the topological dimension of E is the infimum of the Hausdorff dimensions of its homeomorphic images h(E). Later we will discover that Hausdorff dimension is invariant under something slightly stronger - quasi-isometries (sometimes called "bi-Lipschitz maps" or "Lipeomorphic maps"). Indeed, we will see that the equivalence class of quasi-isometric self-similar curves is completely determined by Hausdorff dimension! 5, record 1, English, - Hausdorff%20dimension
Record 1, French
Record 1, Domaine(s)
- Mathématiques
- Infographie
Record 1, Main entry term, French
- dimension de Hausdorff-Besicovitch
1, record 1, French, dimension%20de%20Hausdorff%2DBesicovitch
correct, feminine noun
Record 1, Abbreviations, French
Record 1, Synonyms, French
Record 1, Textual support, French
Record number: 1, Textual support number: 1 DEF
La plus ancienne des dimensions fractales possibles, assignée en 1918 par Felix Hausdorff aux courbes de type flocon de neige et développée en 1935 par Besicovitch. 2, record 1, French, - dimension%20de%20Hausdorff%2DBesicovitch
Record number: 1, Textual support number: 1 OBS
Le concept mathématique «dimension de Hausdorff» constitue une généralisation de la notion de dimension euclidienne. 2, record 1, French, - dimension%20de%20Hausdorff%2DBesicovitch
Record 1, Spanish
Record 1, Textual support, Spanish
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