...uous in the weak (or strong, which is the same in the given case) operator topology. By Stone's theorem, $ U ( t) = e ^ {iAt} $,
3 KB (415 words) - 15:28, 28 February 2022
...a topology (cf. [[Topological structure (topology)|Topological structure (topology)]]) that is compatible with the vector space structure, that is, the follow
with a topology $ \tau $
41 KB (6,085 words) - 08:26, 6 June 2020
...same element of $\mathfrak{A}$. If $\mathfrak{A}$ is endowed with the weak topology (see ), then b) means that the mapping $\R\to\mathfrak{A}$ that takes $t$ t
3 KB (480 words) - 02:51, 15 February 2024
...\overline{G_S G_k} = G_{\mathbf{A}}$? (Here the bar denotes closure in the topology of $G_{\mathbf{A}}$.) If $S = \infty$ ($\infty$ is the set of all Archimede
11 KB (1,671 words) - 18:19, 24 May 2019
...[a8]</TD> <TD valign="top"> D. Sullivan, "Infinitesimal calculations in topology" ''Publ. Math. IHES'' , '''47''' (1977) pp. 269–331</TD></TR></table>
31 KB (4,636 words) - 12:07, 15 December 2019
is a continuous mapping in the topology induced on $ D ^ + $
is valid only in the sense of the weak- topology $ \sigma ( X ^ \prime , X ) $.
34 KB (5,024 words) - 09:12, 21 January 2024
...weak convergence, and in the semi-group of positive-definite functions the topology of uniform convergence on bounded sets.
8 KB (1,162 words) - 19:58, 19 January 2024
...inted out that many theorems are directly related to the geometry and the topology of Banach spaces.
...ar functionals in Banach spaces ultimately evolved to the concept of weak topology. The theory of Banach spaces is a thoroughly studied branch of functional
25 KB (4,253 words) - 23:54, 13 April 2019
converges weakly (see [[#References|[a10]]] and [[Weak topology|Weak topology]]) to $ B _ {P} ( C ) $,
9 KB (1,327 words) - 19:37, 5 June 2020
1) The Lévy metric induces a weak topology in $ {\mathcal F} $(
7 KB (1,007 words) - 04:11, 6 June 2020
...of [[locale]]. The intention was to develop the concept of non-commutative topology introduced by R. Giles and H. Kummer [[#References|[a2]]], while providing
...lign="top"> R. Giles, H. Kummer, "A non-commutative generalization of topology" ''Indiana Univ. Math. J.'' , '''21''' (1971) pp. 91–102</TD></TR>
13 KB (2,065 words) - 18:59, 12 December 2023
...e for the tensor product of $2$-categories, and braid groups" , ''Algebra, Topology, and Category Theory (a collection of papers in honour of Samuel Eilenberg)
18 KB (2,710 words) - 00:41, 15 February 2024
==Topology of $\mathbf{C}$-convex sets.==
...ctions on $E$, endowed with the projective (respectively, inductive) limit topology. An element $\mu$ of the dual space $A ^ { \prime } ( E )$ is called an ana
16 KB (2,533 words) - 09:46, 18 February 2024
...ch case convergence is understood in the sense of the [[Weak topology|weak topology]].
9 KB (1,380 words) - 07:55, 4 March 2022
and the derivative is meant in a topology that is left unspecified. If the mathematical model has been correctly form
in a topology which is the quantum analogue of the probabilistic notion of convergence in
8 KB (1,210 words) - 08:23, 6 June 2020
in the [[Weak topology|weak topology]] $ \sigma ( X , X ^ \prime ) $(
15 KB (2,235 words) - 08:13, 6 June 2020
in the [[Weak topology|weak topology]] induced by $ {\mathcal B} $);
11 KB (1,528 words) - 19:35, 5 June 2020
can be approximated in the strong operator topology by linear operators of finite rank with norm not exceeding 1, and with the
4 KB (651 words) - 15:30, 1 July 2020
...ompact in the weak topology on the dual space, $ $ is also compact in this topology; it is called the maximal ideal space of the algebra $ $ and it is denoted
14 KB (2,175 words) - 17:06, 16 April 2012
The [[Zariski topology|Zariski topology]] on the set of prime ideals (cf. [[Prime ideal|Prime ideal]]) $ \mathop
...ak separation properties (that is, there are non-closed points). A similar topology in the non-commutative case can be introduced on the set $ \mathop{\rm S
7 KB (1,160 words) - 08:00, 6 June 2020