pseudometric topology
21Normal space — Separation Axioms in Topological Spaces Kolmogorov (T0) version T0 | T1 | T2 | T2½ | completely T2 T3 | T3½ | T4 | T5 | T6 In topology and related branches of mathematics, a no …
22Normed vector space — In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… …
23Complete metric space — Cauchy completion redirects here. For the use in category theory, see Karoubi envelope. In mathematical analysis, a metric space M is called complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or,… …
24Baire space — In mathematics, a Baire space is a topological space which, intuitively speaking, is very large and has enough points for certain limit processes. It is named in honor of René Louis Baire who introduced the concept. Motivation In an arbitrary… …
25Hausdorff 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… …
26Gauge space — In topology and related areas of mathematics a gauge space is a topological space where the topology is defined by a family of pseudometrics.A space is uniformizable if and only if it is a gauge space. Examples * A metric space is trivially a… …
27Hemimetric space — In mathematics, a hemimetric space is a generalization of a metric space, obtained by removing the requirements of identity of indiscernibles and of symmetry. It is thus a generalization of both a quasimetric space and a pseudometric space, while …
28Semimetric space — In topology, a semimetric space is a generalized metric space in which the triangle inequality is not required. In translations of Russian texts, a semimetric is sometimes called a symmetric.Note: In functional analysis and related mathematical… …
29Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… …
30Ricci curvature — In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci Curbastro, provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n… …
