property of being a Hausdorff space

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• Hausdorff distance — The Hausdorff distance, or Hausdorff metric, measures how far two compact non empty subsets of a metric space are from each other. It is named after Felix Hausdorff.Informally, the Hausdorff distance between two sets of points, is the longest… …   Wikipedia

• Hausdorff measure — In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in R n or, more generally, in any metric space. The zero dimensional Hausdorff measure is the number of points in …   Wikipedia

• Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

• Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

• Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… …   Wikipedia

• Kolmogorov space — In topology and related branches of mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class of well behaved topological spaces.The T0 condition is one of the separation axioms. Definition A T0 space is a …   Wikipedia

• Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …   Wikipedia

• Extremally disconnected space — In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term extremally disconnected is usual, even though the word extremally does not appear in most… …   Wikipedia

• Locally connected space — In this topological space, V is a neighbourhood of p and it contains a connected neighbourhood (the dark green disk) that contains p. In topology and other branches of mathematics, a topological space X is locally connected if every point admits… …   Wikipedia

• Connected space — For other uses, see Connection (disambiguation). Connected and disconnected subspaces of R² The green space A at top is simply connected whereas the blue space B below is not connected …   Wikipedia

• Local property — In mathematics, a phenomenon is sometimes said to occur locally if, roughly speaking, it occurs on sufficiently small or arbitrarily small neighborhoods of points. Contents 1 Properties of a single space 1.1 Examples 2 Properties of a pair of… …   Wikipedia