...city of their definition, makes them important standard objects in general topology. However, the topological structure of the Tikhonov cubes is far from trivi
2 KB (392 words) - 15:51, 11 August 2014
Define a topology on $ X $
This topology is called the hull-kernel topology on $ X $.
7 KB (1,058 words) - 08:29, 6 June 2020
...$ is dense in $T$. If the algebraic dual $E^*$ of $E$, is given the [[weak topology]] (so that $E^* \simeq \prod_{\alpha \in A} K$,where $K$ is the base field
1 KB (185 words) - 19:44, 27 February 2021
...s functions on the interval $[ 0,1 ]$, with the [[Uniform topology|uniform topology]], the weak convergence
6 KB (857 words) - 21:45, 15 December 2020
...]] on $X$ generated by the family of all superharmonic functions. This new topology was introduced in classical potential theory by Brelot and H. Cartan around
...and $V$ are open in the fine topology, $U$ is a Borel set in the original topology of $X$ and $x \in V \subset U \subset X$.
6 KB (870 words) - 16:57, 1 July 2020
...in the strong operator topology actually converges in the uniform operator topology (see [[#References|[a3]]], [[#References|[a7]]]). In particular, this impli
6 KB (875 words) - 20:01, 27 February 2021
is continuous in the strong topology and sequentially continuous in the weak $ * $
topology of $ \mathfrak X ^ {*} $;
7 KB (1,031 words) - 16:43, 4 June 2020
algebras (weakly Borel, Borel, etc.) that are naturally connected with the topology of $ E $;
endowed with the weak-* topology (so that $ E ^ \prime = V $),
7 KB (1,017 words) - 08:00, 6 June 2020
...the [[Mackey topology]] $\tau(X,X^\alpha)$, or the [[Normal space|normal]] topology is taken. If $X \supset \phi$ and $Y$ are [[BK-space]]s (i.e., Banach [[FK-
3 KB (503 words) - 17:02, 4 October 2017
in the natural weak or uniform topology of the space $ \mathfrak A $
provided with the weak topology, may be considerably strengthened: For any monotone sequence $ f(n) > 0 $
8 KB (1,151 words) - 12:12, 21 March 2022
...respect to the relative $\sigma(F',F)$- (weak) topology on $D(T')$ and the topology on $E'$ of uniform convergence on $\sigma(E,E')$-$K$-convergent sequences.
4 KB (671 words) - 16:06, 20 January 2021
...h space]] possessing a weakly compact subset $K$ (cf. [[Weak topology|Weak topology]]) whose [[linear span]] is dense. These spaces have regularity properties
...ontinuous in the order topology of $[ \omega _ { 0 } , \mu ]$ and the norm topology of $X$, for each $x \in X$. Properties of Banach spaces admitting a project
16 KB (2,514 words) - 19:53, 23 December 2023
|valign="top"|{{Ref|Sp}}||valign="top"| E.H. Spanier, "Algebraic topology", McGraw-Hill (1966) pp. Chapt. 2, §2; Chapt. 7, §2 {{MR|0210112}} {{M
1 KB (187 words) - 22:36, 24 November 2013
...is sufficiently rich and is dense in the set of all distributions with the topology of weak convergence.
2 KB (258 words) - 14:33, 7 October 2014
where the last limit is in the weak topology for probability measures on $\partial \Omega$ (cf. also [[Weak convergence
5 KB (743 words) - 17:01, 1 July 2020
with the usual product topology) is topologically ergodic; equivalently: whenever for every choice of four
5 KB (696 words) - 08:01, 6 June 2020
There is a natural [[Topological structure (topology)|topological structure (topology)]] on $ \Delta ^ {+} $,
namely, the topology of weak convergence (cf. also [[Weak topology|Weak topology]]), where $ F _ {n} \rightarrow F $
12 KB (1,757 words) - 08:07, 6 June 2020
...="top">[a1]</TD> <TD valign="top"> M.J. Greenberg, J.R. Harper, "Algebraic topology, a first course" , Benjamin/Cummings (1981) {{MR|643101}} {{ZBL|0498.55001}
...="top">[a3]</TD> <TD valign="top"> M.J. Greenberg, J.R. Harper, "Algebraic topology, a first course" , Benjamin/Cummings (1981) {{MR|643101}} {{ZBL|0498.55001}
11 KB (1,584 words) - 11:51, 8 April 2023
corresponding topology coincides with the strong topology. The unit
ball $\{f:\|f\|\le 1\}$, considered in the weak topology, is compact.
5 KB (903 words) - 21:31, 3 January 2021
...d fields" C.M. DeWitt (ed.) B.S. DeWitt (ed.) , ''Relativity, groups and topology'' , Gordon & Breach (1964)</TD></TR><TR><TD valign="top">[a4]</TD> <TD
14 KB (2,063 words) - 02:45, 18 July 2022