摘要:

The classical Vitali-Hahn-Saks-Nikodym Theorem [5, Thm. I.4.8] gives a limit criterion for when a sequence of strongly additive vector measures on a σ-field of sets having their range in a Banach space can be expected to be uniformly strongly additive. In [16, Cor. 8], Saeki proved that the limit condition on the sequence of vector measures could be substantially weakened as long as the Banach space in play is “good enough”. Saeki's result was based upon his work on a class of set functions too large to have Rosenthal's Lemma at his disposal. In Section 2, we prove Saeki's result with Rosenthal's Lemma at the basis of our work and then augment our characterization of Banach spaces enjoying Saeki's result in [1] with another natural equivalent condition. In Section 3 we extend Saeki's result to Boolean algebras having the Subsequential Interpolation property.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631985

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We bring to light further infinite dimensional domains with empty interior on which holomorphic maps can be constructed.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631986

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A brief overview of some approaches to cosmological gravitational lensing is given. Emphasis is placed on the geometric structure of our past null cone, particularly the wavefront catastrophes imprinted on it by the hierarchical galaxy distribution. We conjecture on the natural fractal-like limit of this imprinting process and give some applications to studies of the Cosmic Microwave Background (CMB). Finally, some of the outstanding problems in observational cosmology are discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631987

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this paper we exhibit two interlocking sequences in order to study the group ε(X×Y) of based homotopy classes of based self homotopy equivalences of a productX×Yof topological spacesXandY.These sequences have complementary features, and the interconnectedness facilitates computation. The sequences give new results about ε(X×Y) and unify, generalize, and in some cases correct, existing results in the literature about this group. New results include calculations on the group of self equivalences of a product of suspensions (with applications to a product of Moore spaces, includingplocalized spheres); some progress in the computation of non-simply-connected rank 2H-spaces (posed as an open problem in [Ka;problem 5]); and a universal description of ε(Sm×Sn) forn>m≥ 1 as a semidirect product. This last situation includes an example that is not a semidirect product when decomposed in the only other way known (see section 4).

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631988

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Local compactness is studied in the highly convenient setting of semi-uniform convergence spaces which form a common generalization of (symmetric) limit spaces (and thus of symmetric topological spaces) as well as of uniform limit spaces (and thus of uniform spaces). It turns out that it leads to a cartesian closed topological category and, in contrast to the situation for topological spaces, the local compact spaces are exactly the compactly generated spaces. Furthermore, a one-point Hausdorff compactification for noncompact locally compact Hausdorff convergence spaces is considered.1

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631989

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this paper we introduce the notions of uniform complete regularity and uniform normality for nearness frames with the view of obtaining new and pointfree proofs of some known topological results.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631990

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631991

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Köthe type non-Archimedean spaces are introduced in this paper. Bounded sets, compactoid sets, dual spaces, nuclearity, reflexivity and other properties of such spaces are investigated.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631992

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The notion of diminishing orbital diametral sum for a pair of commuting mappings has been introduced into a Hausdorff locally convex space whose topology is generated by a family of seminorms. Subsequently, this notion is utilized to prove common fixed point theorems which generalize certain theorems of Kirk and Tan.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631993

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

If a radical class is closed under involution in every ring with involution then the radical theoretic conditions involving *-bi-ideals are equivalent to the corresponding conditions concerning bi-ideals without involution.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631994

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor