insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article...

weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a...

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. Let...

descriptions as a fallback Topologies on spaces of linear maps Unbounded operator – Linear operator defined on a dense linear subspace Narici & Beckenstein...

a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments...

of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties...

Sobolev spaces. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology is often...

all linear maps φ : V → F {\displaystyle \varphi :V\to F} (linear functionals). Since linear maps are vector space homomorphisms, the dual space may be...

composition of linear maps. If X {\displaystyle X} and Y {\displaystyle Y} are normed spaces, they are isomorphic normed spaces if there exists a linear bijection...

continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a...

set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the...

In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the...

function on its vector space. All linear maps between finite dimensional vector spaces are also continuous. An isometry between two normed vector spaces is...

unique. There exist numerous topologies on any given finite set. Such spaces are called finite topological spaces. Finite spaces are sometimes used to provide...

concrete topologies and topological spaces Modes of convergence (annotated index) – Annotated index of various modes of convergence Topologies on spaces of linear...

subsets Reflexive space – Locally convex topological vector space Semi-reflexive space Strong topology Topologies on spaces of linear maps Schaefer & Wolff...

convex topologies on the vector spaces of a pairing. A pairing is a triple ( X , Y , b ) {\displaystyle (X,Y,b)} consisting of two vector spaces over a...

space topology of uniform convergence on some sub-collection of bounded subsets Strong topology Topologies on spaces of linear maps Weak topology – Mathematical...

spaces should match the topology. For example, instead of considering all linear maps (also called functionals) V → W , {\displaystyle V\to W,} maps between...

topologies on continuous dual space or other topologies on spaces of linear maps. Explicitly, a topological vector spaces (TVS) is complete if every net, or equivalently...

index) – Annotated index of various modes of convergence Net (mathematics) – A generalization of a sequence of points Topologies on spaces of linear maps...

subset of the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological...

In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as...

order topology makes X into a completely normal Hausdorff space. The standard topologies on R, Q, Z, and N are the order topologies. If Y is a subset of X...

bounded family of continuous linear operators between Banach spaces is equicontinuous. Let X and Y be two metric spaces, and F a family of functions from...

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle...

nor σ {\displaystyle \sigma } -quasi-barrelled. Mackey topology Topologies on spaces of linear maps Bourbaki 1987, p. IV.4. Grothendieck 1973, p. 107. Schaefer...

set' is called a topology. A set with a topology is called a topological space. Metric spaces are an important class of topological spaces where a real,...

compactness, were developed in general metric spaces. In general topological spaces, however, these notions of compactness are not necessarily equivalent...

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...