...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
...aracteristic of the field $k$; let $\calF$ be a locally free (in the étale topology) sheaf of $\ZZ/n\ZZ$-modules on $X$; and let $\mu_n$ be the sheaf of $n$-th
...mber-theoretic applications cohomology of sheaves on the flat Grothendieck topology of arithmetic schemes are important. Duality theorems
64 KB (9,418 words) - 12:44, 8 February 2020
Every topology generates a σ-algebra, called Borel σ-algebra. That is, the Borel σ-alge
* the Borel σ-algebra corresponding to the norm topology on $H$;
15 KB (2,605 words) - 07:10, 23 September 2012
...survey of results related to the Dunford–Pettis property" , ''Integration, Topology, and Geometry in Linear Spaces. Proc. Conf. Chapel Hill 1979'' , ''Contemp.
6 KB (912 words) - 13:22, 28 October 2023
...othendieck, "Hodge's general conjecture is false for trivial reasons" ''Topology'' , '''8''' (1969) pp. 299–303</TD></TR><TR><TD valign="top">[a5]</TD>
6 KB (935 words) - 09:01, 21 January 2024
...valence classes of $\mu$-measurable real-valued functions endowed with the topology of convergence in measure relative to each set of finite measure.
16 KB (2,441 words) - 20:16, 25 January 2024
...set of homomorphisms mapping $P ( K )$ onto $\mathbf{C}$, endowed with the topology inherited from the dual space $P ( K ) ^ { * }$. It can be identified with
...ghtarrow \mu _ { z }$ in the weak-$*$ sense (cf. also [[Weak topology|Weak topology]]).
20 KB (3,071 words) - 17:45, 1 July 2020
...gelking, "Transfinite dimension" G.M. Reed (ed.) , ''Surveys in general topology'' , Acad. Press (1980) pp. 131–161</TD></TR><TR><TD valign="top">[3]</T
...> C. Bessaga, A. Pelczyński, "Selected topics in infinite-dimensional topology" , PWN (1975)</TD></TR></table>
15 KB (2,096 words) - 22:12, 5 June 2020
...iven space completely (a ''[[Fréchet–Urysohn space]]'' is one in which the topology is determined by the convergence of sequences) and so the concept of conver
...gence arose in the development of function theory, functional analysis and topology.
22 KB (3,726 words) - 10:31, 2 September 2017
...TR><TR><TD valign="top">[3]</TD> <TD valign="top"> P.S. Urysohn, "Works on topology and other areas of mathematics" , '''1–2''' , Moscow-Leningrad (1951) (In
...but it is just right for algebraic varieties and schemes (with the Zariski topology).
38 KB (5,928 words) - 19:35, 5 June 2020