In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), T2 space or separated space, is...

Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff....

Hausdorff in Wiktionary, the free dictionary. Hausdorff may refer to: A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff"...

In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are...

disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation...

In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and...

In mathematics, the Baker–Campbell–Hausdorff formula gives the value of Z {\displaystyle Z} that solves the equation e X e Y = e Z {\displaystyle e^{X}e^{Y}=e^{Z}}...

Felix Hausdorff (/ˈhaʊsdɔːrf/ HOWS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré...

neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; they are abbreviated as LCH spaces. Let X...

space into a Hausdorff space is a homeomorphism. A compact Hausdorff space is normal and regular. If a space X is compact and Hausdorff, then no finer...

Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions...

neighborhoods. A T3 space or regular Hausdorff space is a topological space that is both regular and a Hausdorff space. (A Hausdorff space or T2 space is a topological...

the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here is a list of fractals, ordered by increasing Hausdorff dimension...

other. Also some authors include some separation axiom (like Hausdorff space or weak Hausdorff space) in the definition of one or both terms, and others...

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)...

The Hausdorff medal is a mathematical prize awarded every two years by the European Set Theory Society. The award recognises the work considered to have...

usual axiom of a manifold to be a Hausdorff space. In general topology, this axiom is relaxed, and one studies non-Hausdorff manifolds: spaces locally homeomorphic...

can be separated by closed neighborhoods. A completely Hausdorff space, or functionally Hausdorff space, is a topological space in which any two distinct...

In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a...

The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere S 2 {\displaystyle {S^{2}}} (the surface of a 3-dimensional...

mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space into...

is also R0. X is Hausdorff, or T2 or separated, if any two distinct points in X are separated by neighbourhoods. Thus, X is Hausdorff if and only if it...

interval and on the paradoxical decompositions of the sphere by Felix Hausdorff, and discussed a number of related questions concerning decompositions...

regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff). Paul Urysohn had used the...

locally Hausdorff if every point has a neighbourhood that is a Hausdorff space under the subspace topology. Every Hausdorff space is locally Hausdorff. There...

example, the definition given by Felix Hausdorff in 1914 is equivalent to the modern definition plus the Hausdorff separation axiom. The separation axioms...

homeomorphic to real n-space Rn. A topological manifold is a locally Euclidean Hausdorff space. It is common to place additional requirements on topological manifolds...

the Hamming distance between two strings of characters, or the Gromov–Hausdorff distance between metric spaces themselves). Formally, a metric space is...

typically denoted ∞. The map c is a Hausdorff compactification if and only if X is a locally compact, noncompact Hausdorff space. For such spaces the Alexandroff...

measure, as described below. Let X {\displaystyle X} be a locally compact Hausdorff space, and let B ( X ) {\displaystyle {\mathfrak {B}}(X)} be the smallest...