insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article...
37 KB (6,521 words) - 12:27, 14 May 2024
weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a...
22 KB (3,110 words) - 12:28, 31 May 2024
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...
10 KB (1,493 words) - 20:43, 17 June 2024
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...
9 KB (1,555 words) - 10:32, 15 January 2024
descriptions as a fallback Topologies on spaces of linear maps Unbounded operator – Linear operator defined on a dense linear subspace Narici & Beckenstein...
30 KB (4,788 words) - 07:22, 7 February 2024
set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the...
18 KB (3,381 words) - 14:09, 28 April 2024
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...
15 KB (2,023 words) - 17:43, 23 May 2024
Sobolev spaces. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology is often...
103 KB (13,527 words) - 03:12, 5 July 2024
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...
103 KB (17,214 words) - 08:06, 6 March 2024
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...
45 KB (6,872 words) - 18:21, 24 June 2024
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...
15 KB (2,716 words) - 12:41, 17 October 2023
continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a...
9 KB (1,196 words) - 06:07, 25 June 2024
Pointwise convergence (redirect from Topology of pointwise convergence)
concrete topologies and topological spaces Modes of convergence (annotated index) – Annotated index of various modes of convergence Topologies on spaces of linear...
8 KB (1,372 words) - 18:59, 22 January 2024
subsets Reflexive space – Locally convex topological vector space Semi-reflexive space Strong topology Topologies on spaces of linear maps Schaefer & Wolff...
11 KB (1,833 words) - 05:17, 16 July 2024
semantics. There exist numerous topologies on any given finite set. Such spaces are called finite topological spaces. Finite spaces are sometimes used to provide...
28 KB (4,033 words) - 15:47, 19 June 2024
index) – Annotated index of various modes of convergence Net (mathematics) – A generalization of a sequence of points Topologies on spaces of linear maps...
7 KB (928 words) - 01:40, 27 February 2024
space topology of uniform convergence on some sub-collection of bounded subsets Strong topology Topologies on spaces of linear maps Weak topology – Mathematical...
6 KB (896 words) - 13:16, 1 June 2024
spaces should match the topology. For example, instead of considering all linear maps (also called functionals) V → W , {\displaystyle V\to W,} maps between...
87 KB (11,431 words) - 05:02, 14 July 2024
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...
91 KB (15,843 words) - 19:08, 25 November 2023
function on its vector space. All linear maps between finite dimensional vector spaces are also continuous. An isometry between two normed vector spaces is...
18 KB (2,890 words) - 22:11, 21 February 2024
In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as...
15 KB (2,586 words) - 09:03, 1 June 2024
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...
43 KB (6,896 words) - 21:17, 7 March 2023
Continuous function (redirect from Continuous maps)
metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology. A stronger...
60 KB (9,404 words) - 15:58, 13 April 2024
Equicontinuity (redirect from Equicontinuous linear maps)
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...
25 KB (3,745 words) - 22:02, 7 June 2023
properties of such objects that are common to all vector spaces. Linear maps are mappings between vector spaces that preserve the vector-space structure...
64 KB (7,774 words) - 15:38, 10 July 2024
nor σ {\displaystyle \sigma } -quasi-barrelled. Mackey topology Topologies on spaces of linear maps Bourbaki 1987, p. IV.4. Grothendieck 1973, p. 107. Schaefer...
3 KB (361 words) - 17:14, 22 February 2023
Tensor product (redirect from Tensor product of linear maps)
{\displaystyle K} represent linear maps of vector spaces, say K n → K n {\displaystyle K^{n}\to K^{n}} , and thus linear maps ψ : P n − 1 → P n − 1 {\displaystyle...
50 KB (8,651 words) - 08:11, 20 June 2024
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...
11 KB (1,565 words) - 00:20, 22 February 2024
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...
15 KB (2,107 words) - 20:11, 16 July 2024
types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"...
69 KB (9,311 words) - 05:27, 20 May 2024