...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
...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
63 KB (9,502 words) - 13:36, 17 October 2019
...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
...alled set-theoretic topology or analytic topology, cf. [[Topology, general|Topology, general]]) tries to explain such concepts as convergence and continuity kn
...ness spaces. The intuitive concept of "nearness" which is fundamental in topology has now found a satisfactory definition: namely, by means of nearness space
57 KB (8,236 words) - 19:41, 20 January 2021
...TR><TD valign="top">[2]</TD> <TD valign="top"> R.M. Switzer, "Algebraic topology - homotopy and homology" , Springer (1975)</TD></TR><TR><TD valign="top">[
9 KB (1,281 words) - 14:40, 21 March 2022
* A [[dense set]] for the [[strong topology]].
...$Y$ and the topology of open sets on $X$ is the pull-back under $f$ of the topology on $Y$. If spaces are quasi=homeomorphic then they are [[lattice equivalen
15 KB (2,305 words) - 11:40, 9 February 2021
...ultrastrong [[Operator topology|operator topology]] (the uniform operator topology does not suffice). A given symmetric [[Banach algebra|Banach algebra]] $
17 KB (2,631 words) - 19:37, 19 January 2024
...The scheme $5$ is defined uniquely up to a local isomorphism in the étale topology [[#References|[1]]]. For the deformation of singular varieties and singular
40 KB (5,788 words) - 13:36, 17 October 2019
is defined uniquely up to a local isomorphism in the étale topology [[#References|[1]]]. For the deformation of singular varieties and singular
41 KB (5,916 words) - 11:24, 26 March 2023
...strong topology if and only if it is separable in the [[Weak topology|weak topology]]; a convex set (in particular, a linear subspace) in a Hilbert space is st
31 KB (4,586 words) - 18:43, 13 January 2024
...ntial theory is characterized by the application of methods and notions of topology and functional analysis, and the use of abstract axiomatic methods (see [[P
38 KB (5,597 words) - 10:29, 30 January 2022
...ext{p} }$ and $\epsilon \in \mathbf{R}$, $\epsilon > 0$. The $\text{p}$-topology has compatible extensions to all sets $V ( \widehat { K } _ { \operatorname
15 KB (2,309 words) - 06:17, 30 June 2024
with respect to the topology of compact convergence; $ I = \{ {f \in {\mathcal O} ( X) } : {f( x) = 0
10 KB (1,513 words) - 08:23, 6 June 2020