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Support (mathematics)

In mathematics, the support of a real-valued function is the subset of the function domain containing the elements which are not mapped to zero. If the domain of is a topological space, then the suppo

Polar topology

In functional analysis and related areas of mathematics a polar topology, topology of -convergence or topology of uniform convergence on the sets of is a method to define locally convex topologies on

Ultraweak topology

In functional analysis, a branch of mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, on the set B(H) of bounded operators on a Hilb

Dual topology

In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a vector space that is induced by the continuous dual of the vector space, by means of the bilin

Topologies on spaces of linear maps

In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can gi

Strong operator topology

In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the

Fredholm kernel

In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral e

Topological vector space

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis.A topologi

Strong dual space

In functional analysis and related areas of mathematics, the strong dual space of a topological vector space (TVS) is the continuous dual space of equipped with the strong (dual) topology or the topol

Compact-open topology

In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of the commonly used topologies on functi

Vague topology

In mathematics, particularly in the area of functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally

Compact convergence

In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology.

Normal family

In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are

Ultrastrong topology

In functional analysis, the ultrastrong topology, or σ-strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the family of seminorms

Function space

In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, t

Weak topology

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most

Uniform limit theorem

In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous.

Epi-convergence

In mathematical analysis, epi-convergence is a type of convergence for real-valued and extended real-valued functions. Epi-convergence is important because it is the appropriate notion of convergence

Pointwise convergence

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compa

Weak operator topology

In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space , such that the functional sending an operator to

Arzelà–Ascoli theorem

The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous funct

Operator topologies

In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach space X.

Uniform convergence

In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function

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