A study of uniformities on the space of uniformly continuous mappings (original) (raw)

Strong and Uniform Continuity – the Uniform Space Case

LMS Journal of Computation and Mathematics, 2003

It is proved, within the constructive theory of apartness spaces, that a strongly continuous mapping from a totally bounded uniform space with a countable base of entourages to a uniform space is uniformly continuous. This lifts a result of Ishihara and Schuster from metric to uniform apartness spaces. The paper is part of a systematic development of computable topology using apartness as the fundamental notion.

Probabilistic uniformities of uniform spaces

2017

Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]quasi-uniformity or a probabilistic uniformity. In 2010, J. Gutiérrez García, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

Some conditions under which a uniform space is fine

1993

Let X be a uniform space of uniform weight µ. It is shown that if every open covering, of power at most µ, is uniform, then X is fine. Furthermore, an ωµ-metric space is fine, provided that every finite open covering is uniform.

Topics in uniform continuity

arXiv (Cornell University), 2011

This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the property of being close to uniformly continuous.

A Reuniformization for Contractive Mappings in Uniform Spaces

Mathematische Nachrichten, 1986

Let S be (t complete uniform HAUSDORFF space with a uniformity generated by a saturated family of pseudometrics %={e,(s, y) : aEA} and let T : X-X be a continuous mapping. The paper contains necessary and sufficient conditions for the existence of a new family of pseudometrics %* ={e."(s, y) : r*EA*} generated the same topology such that T is contractive with respect t o %*.

Some properties of semi-linear uniform spaces

Boletim da Sociedade Paranaense de Matemática, 2011

Semi-linear uniform space is a new space defined by Tallafha, A and Khalil, R in [3], the authors studied some cases of best approximation in such spaces, and gave some open problems in approximation theory in uniform spaces. Besides they defined a set valued map ρ on X × X and asked two questions about the properties of ρ. The purpose of this paper is to answer these questions. Besides we shall define another set valued map δ on X × X and give more properties of semi-linear uniform spaces using the maps ρ and δ. Also we shall give an example of a semi-linear uniform space which is not metrizable.

A new approach to soft uniform spaces

TURKISH JOURNAL OF MATHEMATICS, 2016

The purpose of this paper is to introduce the concept of soft uniform spaces and the relationships between soft uniform spaces and uniform spaces. The notions of soft uniform structure, soft uniform continious function, and operations on soft uniform space are introduced and their basic properties are investigated.