this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

THEOREM 7. IfK is reducible to L and K' to L', then K 0 L is reducible to K' 0 L'. THEOREM 8. For a direct sum I1 + 112 of abelian groups H1 and II2, A0(H11 + II2) is reducible to A0(1) 0 A0(II2). Together with Theorem 2 and the results for cyclic groups, these Theorems prove THEOREM 9. If 11 is a finitely generated abelian group, then any abelian homology or cohomology group A,(II) or Af(II, J...

ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambda-calculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family...

1. Background. The subject of this address is a branch of mathematics which may be regarded as a combination of the classical theory of representations of finite groups by matrices and that part of analysis centering around the theory of Fourier series and integrals. The connection between these two apparently diverse subjects arises simply enough from the fact that the real numbers and the rea...

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈(γ), ∈(γ) ∨ q(δ))-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are intro...

In Theorem 1 the word metric may be replaced, on the one hand, by regular, on the other, by complete metric. This theorem is of interest chiefly because of the similar well known characterizations of the class of all compact metrisable spaces and of the class of all metrisable spaces which are homeomorphic to complete metric spaces.§ The method of proof also relates it to the two characterizati...

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel’skii and Buzyakova.