weaker topology

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• Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia

• Weak operator topology — 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 such that the functional sending an operator T to the complex number is continuous for any… …   Wikipedia

• Operator topology — In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H. Contents 1 Introduction 2 List of topologies on B(H) 3 …   Wikipedia

• Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …   Wikipedia

• Weak topology — This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology. For the weak topology generated by a cover of a space see coherent topology. In mathematics, weak topology… …   Wikipedia

• Base (topology) — In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B. We say that the base generates the topology T. Bases are… …   Wikipedia

• Continuous function (topology) — In topology and related areas of mathematics a continuous function is a morphism between topological spaces. Intuitively, this is a function f where a set of points near f(x) always contain the image of a set of points near x . For a general… …   Wikipedia

• Fine topology (potential theory) — In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, only smooth functions were considered, namely those for… …   Wikipedia

• Nisnevich topology — In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic K theory, A¹ homotopy theory, and the theory of motives. It …   Wikipedia

• Strong operator topology — In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map… …   Wikipedia

• Fork (topology) — The notion of a fork appears in the characterization of graphs, including network topology, and topological spaces.A graph has a fork in any vertex which is connected by three or more edges. Correspondingly, a topological space is said to have a… …   Wikipedia