In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators...

In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H...

Then the topology τ1 is said to be a coarser (weaker or smaller) topology than τ2, and τ2 is said to be a finer (stronger or larger) topology than τ1....

} there is a topology weaker than the weak topology of X ′ , {\displaystyle X',} called the weak* topology. It is the coarsest topology on X ′ {\displaystyle...

a range of locally convex topologies. Such topologies are called polar topologies. The weak topology is the weakest topology of this range. Throughout...

In mathematics, weak convergence in a Hilbert space is the convergence of a sequence of points in the weak topology. A sequence of points ( x n ) {\displaystyle...

normed vector space is compact in the weak* topology. A common proof identifies the unit ball with the weak-* topology as a closed subset of a product of...

related areas of mathematics a polar topology, topology of G {\displaystyle {\mathcal {G}}} -convergence or topology of uniform convergence on the sets...

mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, is a topology on B(H), the space of bounded...

topology.) The σ-weak topology or ultraweak topology or weak-* operator topology or weak-* topology or weak topology or σ(B(H), B(H)*) topology is defined by...

if its topology is the same as the Mackey topology. The Mackey topology is the opposite of the weak topology, which is the coarsest topology on a topological...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

smaller complex). The C in CW stands for "closure-finite", and the W for "weak" topology. A CW complex is constructed by taking the union of a sequence of topological...

operator topology Topologies on spaces of linear maps Ultrastrong topology Ultraweak topology/weak-* operator topology Weak operator topology Inductive...

probability measures Weak convergence (Hilbert space) of a sequence in a Hilbert space more generally, convergence in weak topology in a Banach space or...

a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on...

{\displaystyle J,} but the topology on X {\displaystyle X} (the weak topology of Y {\displaystyle Y} ) is not the strong topology β ( X , X ′ ) , {\displaystyle...

of various modes of convergence Topologies on spaces of linear maps Weak topology – Mathematical term Weak-* topology – Mathematical termPages displaying...

topology if and only if ‖ T i x − T x ‖ → 0 {\displaystyle \|T_{i}x-Tx\|\to 0} for each x in H. The SOT is stronger than the weak operator topology and...

and statistics, weak convergence is one of many types of convergence relating to the convergence of measures. It depends on a topology on the underlying...

possible dual topologies on a locally convex space. The theorem shows that the coarsest dual topology is the weak topology, the topology of uniform convergence...

dual topology; if the topology is instead the weak-* topology then this will be indicated. Neither topology is metrizable although unlike the weak-* topology...

{\displaystyle \beta \left(X^{\prime },X\right).} The coarsest polar topology is called weak topology. The strong dual space plays such an important role in modern...

has two natural topologies: weak and strong (Hirsch 1997). When the manifold is compact, these two topologies agree. The weak topology is always metrizable...

on A {\displaystyle A} ; moreover, when equipped with the relative weak-* topology, Φ A {\displaystyle \Phi _{A}} turns out to be locally compact and...

natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which...

functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally compact...

topology possible on a given set Weak topology, an example of topology coarser than the standard one Fine topology (disambiguation) This disambiguation...

Uniform norm Weak topology Strong topology Hilbert cube Lower limit topology Sorgenfrey plane Real tree Compact-open topology Zariski topology Kuratowski...

*-representations of A on Hn with the point-weak topology. In terms of convergence of nets, this topology is defined by πi → π; if and only if ⟨ π i (...