Search results for "Topological tensor product"

On distinguished polynomials and their projections

2012

We study projections and injections between projective tensor products spaces or spaces of polynomials and we show that the example of a polynomial constructed in (4), that is neither p-dominated nor compact, can be identified with the projection map of the symmetric tensor product onto the space. Also we give a characterization of the weak and quasi approximation properties on symmetric tensor products.

Sobolev Spaces and Quasiconformal Mappings on Metric Spaces

2001

Heinonen and I have recently established a theory of quasiconformal mappings on Ahlfors regular Loewner spaces. These spaces are metric spaces that have sufficiently many rectifiable curves in a sense of good estimates on moduli of curve families. The Loewner condition can be conveniently described in terms of Poincare inequalities for pairs of functions and upper gradients. Here an upper gradient plays the role that the length of the gradient of a smooth function has in the Euclidean setting. For example, the Euclidean spaces and Heisenberg groups and the more general Carnot groups admit the type of a Poincare inequality we need. We describe the basics and discuss the associated Sobolev sp…

THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

2013

On inductive dimensions for fuzzy topological spaces

1995

An approach to the dimension theory for fuzzy topological spaces is being developed. The appropriate context for this theory is not the category CFT of Chang fuzzy topological spaces or some of its modifications, but the category Hut introduced in the paper (this category is a slight extension of the category H of Hutton fuzzy topological spaces Hutton (1980). The frames of this category allow us to make exposition simple and uniform, and on the other hand to make it applicable in quite a general setting.

Noetherian type in topological products

2010

The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …

Localification of variable-basis topological systems

2011

The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh and shows that the procedure of localification is possible in the new setting. Quaestiones Mathematicae 33(2010), 11–33