Urysohn and completely Hausdorff spaces information

Urysohn space, or T2½ space, is a topological space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff...

preregular space is completely regular. Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have...

completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces. A topological space X is a normal space if, given any...

spaces that are not Tychonoff (i.e. not Hausdorff). Paul Urysohn had used the notion of completely regular space in a 1925 paper without giving it a name...

-Hausdorff spaces are to Δ {\displaystyle \Delta } -generated spaces as weak Hausdorff spaces are to compactly generated spaces. Fixed-point space –...

concepts of Fréchet–Urysohn spaces, T-sequential spaces, and N {\displaystyle N} -sequential spaces are also defined in terms of how a space's topology interacts...

introduced by Pavel Alexandrov and Pavel Urysohn in 1929, exhibits compact spaces as generalizations of finite sets. In spaces that are compact in this sense,...

for topological spaces that hold for both regular and Hausdorff spaces. Most of the time, these results hold for all preregular spaces; they were listed...

Alexandroff and Paul Urysohn, was based heavily on Hausdorff's Principles. This is shown by the surviving correspondence in Hausdorff's Nachlass with Urysohn, and...

characterized by being Hausdorff and having a bounded convex neighborhood of the origin. All Banach spaces are barrelled spaces, which means that every...

the term T1 space is preferred. There is also a notion of a Fréchet–Urysohn space as a type of sequential space. The term symmetric space also has another...

Polish spaces, locally compact spaces that are metrizable and countable at infinity, countable intersections of Polish subspaces of a Hausdorff topological...

neighbourhoods. Thus, X is Hausdorff if and only if it is both T0 and R1. Every Hausdorff space is also T1. X is T2½, or Urysohn, if any two distinct points in...

neighborhood not containing the other, are T0 spaces. This includes all T2 (or Hausdorff) spaces, i.e., all topological spaces in which distinct points have disjoint...

Steen and Seebach define a Urysohn space as "a space with a Urysohn function for any two points". Willard calls this a completely Hausdorff space. Steen...

Normal Hausdorff. A normal space is Hausdorff if and only if it is T1. Normal Hausdorff spaces are always Tychonoff. Completely normal. A space is completely...

mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes...

locally Hausdorff. There are locally Hausdorff spaces where a sequence has more than one limit. This can never happen for a Hausdorff space. The line...

confused with separated spaces (defined below), which are somewhat related but different. Separable spaces are again a completely different topological...

mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions...

in general topological spaces, limits of sequences need not be unique. However, often topological spaces must be Hausdorff spaces where limit points are...

use the terms T3, T4, and T5 to refer to regular, normal, and completely normal. They also refer to completely Hausdorff as Urysohn. This was a result of...

B} if and only if their closures intersect. More generally, proximities classify the compactifications of a completely regular Hausdorff space. A uniform...

normal subgroup). Uniform spaces generalize both pseudometric spaces and topological groups. In a uniform space, x ≡ y if and only if the pair (x, y) belongs...

space Lindelöf space Sigma-compact space Connected space T0 space T1 space Hausdorff space Completely Hausdorff space Regular space Tychonoff space Normal...