normed topology
41Metric (mathematics) — In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric …
42Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …
43Modes of convergence — In mathematics, there are many senses in which a sequence or a series is said to be convergent. This article describes various modes (senses or species) of convergence in the settings where they are defined. For a list of modes of convergence,… …
44Neighbourhood system — In topology and related areas of mathematics, the neighbourhood system or neighbourhood filter for a point x is the collection of all neighbourhoods for the point x. A neighbourhood basis or local basis for a point x is a filter base of the… …
45Gelfand representation — In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings:* a way of representing commutative Banach algebras as algebras of continuous functions; * the fact that for commutative C*… …
46Hahn–Banach theorem — In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear operators defined on a subspace of some vector space to the whole space, and it also shows that there are enough… …
47Projection (linear algebra) — Orthogonal projection redirects here. For the technical drawing concept, see orthographic projection. For a concrete discussion of orthogonal projections in finite dimensional linear spaces, see vector projection. The transformation P is the… …
48Classical Wiener space — In mathematics, classical Wiener space is the collection of all continuous functions on a given domain (usually a sub interval of the real line), taking values in a metric space (usually n dimensional Euclidean space). Classical Wiener space is… …
49Group algebra — This page discusses topological algebras associated to topological groups; for the purely algebraic case of discrete groups see group ring. In mathematics, the group algebra is any of various constructions to assign to a locally compact group an… …
50Compactly embedded — In mathematics, the notion of being compactly embedded expresses the idea that one set or space is well contained inside another. There are versions of this concept appropriate to general topology and functional analysis. Definition (topological… …
