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Übersetzung für 'Hausdorff' von Englisch nach Deutsch

Hausdorff dimension

Hausdorff-Dimension {f}math.

Hausdorff property

Hausdorffeigenschaft {f} [auch: Hausdorff-Eigenschaft]math.

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Hausdorff space

Hausdorff-Raum {m}math.

hausdorffscher Raum {m}math.

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Hausdorff maximal principle

Maximalkettenprinzip {m} (von Hausdorff) [auch: Hausdorff'sches Maximalkettenprinzip]math.

Hausdorff maximality theorem

(Hausdorffs) Maximalkettensatz {m}math.

Hausdorff maximality theorem [Hausdorff maximal principle]

Maximalitätsprinzip {n} von Hausdorffmath.

Hausdorff separation axiom [Hausdorff space]

Hausdorff'sches Trennungs­axiom {n}math.

Hausdorff-Young inequality

Hausdorff-Young-Ungleichung {f}math.

paracompact Hausdorff space

parakompakter Hausdorff-Raum {m}math.

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Baker-Campbell-Hausdorff formula

Baker-Campbell-Hausdorff-Formel {f}math.

• Hausdorff-Dimension {f} = Hausdorff dimension
• Hausdorff-Raum {m} = Hausdorff space
• Hausdorff'scher Raum {m} = T2 space [Hausdorff space]

• Because non-Hausdorff manifolds are locally homeomorphic to Euclidean space, they are locally metrizable (but not metrizable) and locally Hausdorff (but not Hausdorff).
• Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.
• Conversely, every compactly generated Hausdorff space is a quotient of some locally compact Hausdorff space.
• For example, in a non-hausdorff space, it is possible for a sequence to converge to multiple different limits.
• Every Hausdorff space is necessarily sequentially Hausdorff. A sequential space is Hausdorff if and only if it is sequentially Hausdorff.

• Note that the theorem still holds (perhaps vacuously) for "X" an arbitrary Hausdorff space and "Y" a Hausdorff space with countable π-base.
• A variant of Falconer's conjecture states that, for points in the plane, a compact set whose Hausdorff dimension is greater than or equal to one must have a distance set of Hausdorff dimension one.
• Any product of Hausdorff spaces is again a Hausdorff space.
• In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence.
• Since the only Hausdorff topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily be discrete.

• This subsection details how every non-Hausdorff TVS [...] can be TVS-embedded onto a dense vector subspace of a complete TVS.
• There exist spaces which are Hausdorff but not Urysohn, and spaces which are Urysohn but not completely Hausdorff or regular Hausdorff. Examples are non trivial; for details see Steen and Seebach.
• However, the compact Hausdorff spaces are "absolutely closed", in the sense that, if you embed a compact Hausdorff space [...] in an arbitrary Hausdorff space [...] then [...] will always be a closed subset of [...]; the "surrounding space" does not matter here.
• The topology [...] need not be Hausdorff but [...] is Hausdorff.