weak topology


Also found in: Wikipedia.

weak topology

[′wēk tə′päl·ə·jē]
(mathematics)
A topology on a topological vector space X whose open neighborhoods around a point x are obtained from those points y of X for which every ƒi (x) is close to ƒi (y), ƒi appearing in a finite list of linear functionals.
Mentioned in ?
References in periodicals archive ?
On the other hand, by construction [tau] is weaker than the weak topology [sigma](E*, E**).
o]; d [member of] D} is dense in [OMEGA]* in the weak topology.
Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory Under Weak Topology for Nonlinear Operators and Black Operator Matrices With Applications
If K is a weakly compact subset of E and K with the relative weak topology is metrizable (for example E could be a Banach space whose dual [E.
2 serves to the purpose: one considers E endowed with the weak topology and identify E* with E.
with respect to the weak topology, see [3], then there exists a sequence [([[phi].
We commence this work with the following proposition which shows that we can consider the topology [beta](X) as a weak topology under all left multipliers induced by a function space on M(X).
n])]) converges to 0 for the weak topology [sigma](E, E') whenever the sequence ([x.
E endowed with the weak topology [sigma] (E, E') is a K-analytic space.
alpha]]} converges to 0 in the weak topology of [L.
every convergent sequence in the weak topology of C(X, K) is norm-convergent, see [14, Corollary 2.
Then the weak topology of X is the product of the weak topology of [M.