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Definition of hausdorff in English English dictionary
- Such that any two points have disjoint neighborhoods
- Such that any two points have disjoint neighborhoods: said of a topological space
- Hausdorff content
- the d-dimensional Hausdorff content of S is defined by C_H^d(S): =\lim_{\sup_i r_i \rightarrow 0} \inf\Bigl\{\sum_i r_i^d: \text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}
- Hausdorff dimension
- A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero
- Hausdorff metric
- In the abstract metric space of all compact subsets of \mathbb{R}^n, given a pair of compact sets A and B, the Hausdorff metric is h(A,B) = \mbox{max} \{\rho(A,B), \rho(B,A)\} where \rho(A,B) = \sup_{a\in A} \inf_{b\in B} \, d(a,b) , where d is the Euclidean metric in \mathbb{R}^n
h(A,B) = 0 iff A = B.
- Hausdorff space
- A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x \in U and y \in V
Related Terms
hausdorff
Synonyms
t₂Etymology
() From the eponym Felix Hausdorff (1868–1942).Resimler
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