In functional analysis and related areas of mathematics an absorbing set in a vector space is a setS which can be inflated to include any element of the vector space. Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... In mathematics, a vector space (or linear space) is a collection of objects (known as vectors) which may be scaled and added; all linear combinations of vectors are themselves vectors. ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ...
Given a vector space X over a fieldF a set S is called absorbing if for all there exists a real number r such that This article presents the essential definitions. ...
In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the length of a vector is intuitive and can be easily extended to any real vector space Rn. ... some unit spheres In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used. ...
Properties
the finite intersection of absorbing sets is absorbing
In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. ...
In functional analysis and related areas of mathematics an absorbingset in a vector space is a set S which can be inflated to include any element of the vector space.
In a semi normed vector space the unit ball is absorbing.
the finite intersection of absorbingsets is absorbing
This implies that an absorbingset does not have to be connected, convex.
For an example of an absorbingset that is not circled, take the union of a unit disk and an annulus centered at 0 that is large enough so it is disjoint from the disk.
This is version 6 of absorbingset, born on 2005-08-02, modified 2005-08-03.
there exists a real number r such that
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