absolutely convex

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English-Russian scientific dictionary. 2008.

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  • Absolutely convex set — A set C in a real or complex vector space is said to be absolutely convex if it is convex and balanced. Properties A set C is absolutely convex if and only if for any points x 1, , x 2 in C and any numbers lambda 1, , lambda 2 satisfying |lambda… …   Wikipedia

  • Convex set — A convex set …   Wikipedia

  • Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia

  • Norm (mathematics) — This article is about linear algebra and analysis. For field theory, see Field norm. For ideals, see Norm of an ideal. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional… …   Wikipedia

  • Polar set — See also polar set (potential theory). In functional analysis and related areas of mathematics the polar set of a given subset of a vector space is a certain set in the dual space.Given a dual pair (X,Y) the polar set or polar of a subset A of X… …   Wikipedia

  • Bounded set (topological vector space) — In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. Conversely a set which is not… …   Wikipedia

  • Dual topology — In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair, two vector spaces with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space.… …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • Tsirelson space — In mathematics, Tsirelson space T is an example of a reflexive Banach space in which neither an l p space nor a c 0 space can be embedded.It was introduced by B. S. Tsirelson in 1974. In the same year, Figiel and Johnson published a related… …   Wikipedia

  • Balanced set — In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K with an absolute value |.|) is a set S so that for all scalars α with |α| ≤ 1 with The balanced hull or balanced envelope for …   Wikipedia

  • Mackey topology — In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not… …   Wikipedia


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