Beshimov, R. B. Safarova, D. T.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, the connection between a finally compact, pceudocompact, extremely disconnected, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph$$\end{doc...

Beshimov, R. B. Georgiou, Dimitrios N. Zhuraev, R. M.

In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) â†’ (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : ...

Bouziad, Ahmed

A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is functionally generated by its precompact subsets is proximally fine with respect to its right uniformity. On the other hand, we show th...

Coghetto, Roland
Published in
Formalized Mathematics

In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. ...

Coornaert, Michel Ceccherini-Silberstein, Tullio

A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are ...

Ceccherini-Silberstein, Tullio Coornaert, Michel
Published in
Journal of Dynamical and Control Systems

We give sufficient conditions for sensitivity of continuous group actions on uniform spaces.

Włodarczyk, Kazimierz Plebaniak, Robert
Published in
Fixed Point Theory and Applications

In uniform spaces, using J-families of generalized pseudodistances, we construct four kinds of contractions of Kannan type and, by techniques based on these generalized pseudodistances, we prove fixed point theorems for such contractions. The results are new in uniform and locally convex spaces and even in metric spaces. Examples are given. MSC: 47...

Mishra, Swaminath Singh, Shyam Lal Stofile, Simfumene
Published in
Fixed Point Theory and Applications

Stability results for a pair of sequences of mappings and their common fixed points in a Hausdorff uniform space using certain new notions of convergence are proved. The results obtained herein extend and unify several known results. AMS(MOS) Subject classification 2010: 47H10; 54H25.

Pin, Jean-Eric Silva, Pedro

We consider uniformities associated with a variety of finite monoids V, but we work with arbitrary monoids and not only with free or free profinite monoids. The aim of this paper is to address two general questions on these uniform structures and a few more specialized ones. A first question is whether these uniformities can be defined by a metric ...

Tret’yachenko, Yu. V.
Published in
Russian Mathematics

In this paper we consider sequences of functions that are defined on a subset of the real line and take on values in a uniform Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences. We prove that this generalization of the Helly theorem includes many results of the recent researc...