Hausdorff may refer to:
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space ( , ), separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each which are disjoint from each other. Of the many ...
, when used as an adjective, as in "the real line is Hausdorff"
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Felix Hausdorff
Felix Hausdorff ( , ; November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and ...
(1868–1942), the German mathematician after whom Hausdorff spaces are named
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Hausdorff dimension
In mathematics, Hausdorff dimension is a measure of ''roughness'', or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a ...
, a measure theoretic concept of dimension
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Hausdorff distance In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric ...
or Hausdorff metric, which measures how far two compact non-empty subsets of a metric space are from each other
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Hausdorff density In measure theory, a field of mathematics, the Hausdorff density measures how concentrated a Radon measure is at some point.
Definition
Let \mu be a Radon measure and a\in\mathbb^ some point in Euclidean space. The ''s''-dimensional upper and l ...
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Hausdorff maximal principle
In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained ...
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Hausdorff measure
In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions. It is a type of outer measure, named for Felix Hausdorff, that ass ...
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Hausdorff moment problem In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments
:m_n = \int_0^1 x^n\,d\mu(x)
of some Borel measure supported on the clo ...
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Hausdorff paradox The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere (a 3-dimensional sphere in ). It states that if a certain countable subset is removed from , then the remainder can be divided into three disjoin ...
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