...ner by a fixed differential expression on some set, open in an appropriate topology, of infinitely (or sufficiently often) differentiable sections of a given v
17 KB (2,519 words) - 19:35, 5 June 2020
...M} ( S )$ is bounded above by some constant $c$, form a compact set. (The topology is that generated by the integral flat distance, defined for $m$-integral c
...}$.) The space of $m$-varifolds is equipped with the [[Weak topology|weak topology]] given by saying that $\nu _ { i } \rightarrow \nu$ if and only if $\int f
21 KB (3,319 words) - 17:46, 1 July 2020
...<td valign="top"> R. Brown, "Groupoids and crossed objects in algebraic topology" ''Homology, Homotopy and Appl.'' , '''1''' (1999) pp. 1–78</td></tr><
13 KB (1,937 words) - 13:10, 24 December 2020
..., and for this reason they make it possible to solve problems of homotopic topology that are not solvable "at the level" of cohomology groups. Examples. 1) L
...top">[4]</TD> <TD valign="top"> S.P. Novikov, "The methods of algebraic topology from the viewpoint of cobordism theory" ''Math. USSR.-Izv.'' , '''31''' (
29 KB (4,197 words) - 09:49, 26 March 2023
...s differentiable in $ C ^ \infty ( G) $ (with respect to the standard topology in $ C ^ \infty ( G) $:
the topology of compact convergence). Every continuous [[Finite-dimensional representati
32 KB (4,602 words) - 04:46, 7 January 2022
...olev spaces, the space $C^\infty (\Omega)$ is ''not dense'' in the strong topology: its strong closure is instead $W^{1,1} (\Omega)$.
...space by $SBV (\Omega)$. Though this space is not closed in the weak$^*$ topology, Ambrosio discovered that it still has a useful closure property, suitable
49 KB (8,072 words) - 20:25, 12 March 2020
...e of $\{ \mu _ { n } \}$ converges (in an appropriate [[Weak topology|weak topology]]) to a representing measure $\mu$ for $\gamma$ with $\operatorname{supp} \
23 KB (3,450 words) - 17:45, 1 July 2020
$H_n(\theta)$ is continuous in $\theta$, in the topology of weak
14 KB (2,104 words) - 19:26, 4 March 2024
where the vectors on the right-hand side converge in the strong Hilbert space topology. The asymptotic fields $A ^ { \text { in/out } } ( f )$ are free fields and
9 KB (1,385 words) - 20:57, 8 February 2024
...ll be considered. It has turned out to be useful not only in set-theoretic topology, but also in the geometry of Banach spaces, non-linear analysis, number the
10 KB (1,579 words) - 17:01, 1 July 2020
The topology of $ C ^ \prime (G) $
equipped with the compact-open topology. Various subalgebras of $ M (G) $
20 KB (2,775 words) - 16:40, 31 March 2020
...ed with measures defined on sets connected in some way or another with the topology of the underlying space. One of the typical approaches is the following. Le
is usually endowed with the weak topology $ w $,
46 KB (7,065 words) - 19:30, 1 January 2021
...org/legacyimages/h/h046/h046320/h046320110.png" /> with the usual Gel'fand topology (the so-called Corona problem) was solved affirmatively on the basis of a d
37 KB (5,073 words) - 18:20, 1 December 2014
...<TD valign="top"> D. Sullivan, "Quasiconformal homeomorphisms in dynamics, topology and geometry" A.M. Gleason (ed.) , ''Proc. Internat. Congress Mathematician
12 KB (1,685 words) - 08:27, 6 June 2020
...$\sup a = \gamma$; it is closed in $\gamma$ if it is closed in the [[order topology]] on $\gamma$: that is, for any limit $\mu < \gamma$ with $\sup(a\cap\mu) =
...es" in Crosilla, Laura and Schuster, Peter (edd.) ''From sets and types to topology and analysis. Towards practicable foundations for constructive mathematics'
33 KB (5,106 words) - 18:44, 3 July 2021
...which has no compact factors. Then $\Gamma$ is dense in $G$ in the Zariski topology
20 KB (3,146 words) - 02:52, 23 July 2018
tend to zero in the strong operator topology (such operators form the class $ C _ {00} $),
24 KB (3,593 words) - 18:51, 13 January 2024
Equations constituting a breakthrough in work on the topology of four-dimensional manifolds (cf. also [[Four-dimensional manifold|Four-di
...align="top"> S.K. Donaldson, "The Seiberg–Witten equations and 4-manifold topology" ''Bull. Amer. Math. Soc.'' , '''33''' (1996) pp. 45–70</TD></TR>
16 KB (2,663 words) - 10:57, 13 February 2024
[[Algebraic topology]] |
[[Differential topology]] |
15 KB (1,797 words) - 15:27, 6 May 2012
Besides this, in the theory of linear operators between spaces with a topology there are important problems of approximating various classes of linear ope
...The problem of calculating their index required the apparatus of algebraic topology [[#References|[8]]] (cf. also [[Index formulas|Index formulas]]).
67 KB (9,247 words) - 17:12, 29 October 2017