...erator topology follows its continuity with respect to the strong operator topology; for a unitary representation one can define the operation of tensor produc
...1 at the unit element of the group, the [[Topology of uniform convergence|topology of uniform convergence]] on compact subsets of $ G $
24 KB (3,516 words) - 08:27, 6 June 2020
...a group of automorphisms that is continuous with respect to the ultraweak topology on $\mathcal{X}$. Since these groups are isometric, in this discussion it i
...G }$ is an isometric representation of $G$ that is continuous in the weak topology, then for each finite regular [[Borel measure|Borel measure]] $\mu$ on $G$
14 KB (2,151 words) - 17:43, 1 July 2020
with the weak topology. For any real $ \lambda $,
This subset is endowed with a Polish (or Suslin) topology such that any $ u \in U $
8 KB (1,190 words) - 08:16, 20 January 2024
...G} $ is an isometric representation of $G$ that is continuous in the weak topology, then for each finite regular Borel measure $\mu$ on $G$ there is an opera
4 KB (640 words) - 17:31, 15 May 2014
be their duals endowed with the strong topology, let $ L ( E, F ) $
in the topology of uniform convergence on bounded sets. Thus, in this topology, the nuclear operator $ A $
24 KB (3,574 words) - 18:23, 21 January 2021
...es are usually distinguished in variational calculus — a strong and a weak topology and, correspondingly, one defines strong and weak extrema. For instance, as
...iational calculus and the qualitative theory of differential equations and topology. The development of functional analysis made a substantial contribution to
28 KB (4,182 words) - 07:56, 16 April 2023
...clopediaofmath.org/legacyimages/g/g043/g043810/g04381016.png" />, with the
topology given by the countable set of norms
...encyclopediaofmath.org/legacyimages/g/g043/g043810/g043810337.png" />. The
topology of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.or
74 KB (9,823 words) - 19:33, 9 November 2014
...thcal{L} _ { \mathbf{C} } ^ { 1 } ( G ) )$ coincides with the compact-open topology on $G$ ([[#References|[a3]]]; see also [[#References|[a9]]], [[#References|
7 KB (1,059 words) - 15:30, 1 July 2020
Low-dimensional topology enters bicategory theory from two dual directions. The commutative diagrams
...al group theory" R. Brown (ed.) T.L. Thickstun (ed.) , ''Low dimensional topology'' , ''Lecture Notes London Math. Soc.'' , '''48''' , Cambridge Univ. Press
24 KB (3,338 words) - 17:29, 7 February 2011
...discrete topology]]. There exist semi-groups which admit only the discrete topology. Any Hausdorff space can be made into a topological semi-group, e.g. by giv
becomes a connected topological semi-group under the order (interval) topology. A semi-group $ S $
16 KB (2,287 words) - 14:36, 19 March 2023
...ntable sequence of operators of finite rank in the strong or weak operator topology [[#References|[6]]]. Nuclear Fréchet spaces without a Schauder [[Basis|bas
equipped with the topology of uniform convergence of all derivatives on compact subsets of $ \mathbf
26 KB (3,852 words) - 07:00, 6 May 2022
with a topology $ {\mathcal C} $
...). Conversely, a standard Markov process is a Feller process for a natural topology $ {\mathcal C} _ {0} $;
11 KB (1,576 words) - 19:38, 5 June 2020
...onvergence of operators on such a space (cf. also [[Strong topology|Strong topology]]) implies [[Uniform convergence|uniform convergence]]. For example, let $
8 KB (1,247 words) - 12:01, 26 March 2023
which is compatible with the topology there corresponds a unique compactification $ b _ \delta X $
which are compatible with the topology, and the set $ B( X) $.
25 KB (3,639 words) - 09:53, 26 March 2023
symmetric probability measures with the weak topology. The De Finetti theorem for $ m $-
13 KB (1,888 words) - 11:23, 26 March 2023
...eak topology on the dual space. Since the unit ball is compact in the weak topology on the dual space, $ \Phi $
is also compact in this topology; it is called the maximal ideal space of the algebra $ A $
18 KB (2,806 words) - 03:47, 25 February 2022
...: A topos is a category $\mathcal C$ such that any sheaf for the canonical topology on $\mathcal C$ is representable. For the objects of a topos (which are she
...étale and crystalline cohomologies of a scheme (cf. [[Etale topology|Etale topology]]). Although such cohomology can be described directly in terms of a given
10 KB (1,557 words) - 09:21, 1 May 2021
...enetrated almost all branches of mathematics. In conjunction with algebra, topology forms a general foundation of mathematics, and promotes its unity.
...e mappings that are continuous together with their inverses. Consequently, topology can be qualified as a branch of geometry. An important feature of this geom
38 KB (5,626 words) - 17:15, 20 March 2018
...ized function|Support of a generalized function]]). It is endowed with the topology of the strong inductive limit of the (increasing) sequence of spaces $ C
12 KB (1,594 words) - 17:37, 1 February 2022
A basis for a topology of a topological space $ X $(
...additional restrictions (e.g. an order) and additional structures (e.g. a topology) are imposed on $ T $,
28 KB (4,564 words) - 07:37, 26 March 2023