منابع مشابه
Spaces of Valuations
Valuations are measure like functions mapping the open sets of a topological space into positive real numbers They can be classi ed according to some additional properties Some topological spaces are de ned whose elements are valuations from various classes The relationships among these spaces are studied and universal properties are shown for some of them
متن کاملValuations on Sobolev Spaces
All affinely covariant convex-body-valued valuations on the Sobolev space W (R) are completely classified. It is shown that there is a unique such valuation for Blaschke addition. This valuation turns out to be the operator which associates with each function f ∈W (R) the unit ball of its optimal Sobolev norm. 2000 AMS subject classification: 46B20 (46E35, 52A21,52B45) Let ‖ ·‖ denote a norm on...
متن کاملs-Topological vector spaces
In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...
متن کاملValuations and hyperplanes of dual polar spaces
Valuations were introduced in De Bruyn andVandecasteele (Valuations of near polygons, preprint, 2004) as a very important tool for classifying near polygons. In the present paperwe study valuations of dual polar spaces.Wewill introduce the class of theSDPS-valuations and characterize these valuations. We will show that a valuation of a finite thick dual polar space is the extension of an SDPS-v...
متن کاملLOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES
In this paper, the concept of {sl local base with stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1975
ISSN: 0021-8693
DOI: 10.1016/0021-8693(75)90033-2