A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n = 0, 1, 2, . . ., every locally אn-bounded topological group is either precompact or ambitable. In the familiar semigroups constructed over ambitable groups, topological centres have an effective characterization.

1 Instituto de Productos Lácteos de Asturias, Consejo Superior de Investigaciones Cient́ıficas (IPLA-CSIC), Paseo Rı́o Linares s/n, Villaviciosa, 33300 Asturias, Spain 2Food Safety Programme, ESR-Christchurch Science Centre, Christchurch 8540, New Zealand 3Food and Environment Safety, The Food and Environment Research Agency, Sand Hutton, York YO41 ILZ, UK 4Medical Nutrition Physiology Group, Pha...

The notion of completeness in metric spaces and that of completing a metric space are traditionally discussed in terms of Cauchy sequences. The main reason being that this concept deals precisely with the issue of convergence of sequences in the sense that every convergent sequence is a Cauchy sequence. The paper deals with completion in a setting that avoids explicit reference to Cauchy sequen...

Controlled trials have shown that the rate of healing of gastric ulcers is increased by treatment with carbenoxolone sodium, but that fluid retention is produced as a side effect sufficiently often to limit the freedom with which the drug can be prescribed (Doll, Hill, Hutton, and Underwood, 1962; Doll, Hill, and Hutton, 1965; Horwich and Galloway, 1965). We have, therefore, sought a method of ...

We revisit the work of Paterson and of Meijer & Hutton, which describes how to construct catamorphisms for recur-sive datatype deenitions that embed contravariant occurrences of the type being deened. Their construction requires , for each catamorphism, the deenition of an anamor-phism that has an inverse-like relationship to that cata-morphism. We present an alternative construction, which rep...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...