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Suzuki type fuzzy 𝒵 -contractive mappings and fixed points in fuzzy metric spaces

Dhananjay Gopal, Juan Martínez-Moreno (2021)

Kybernetika

In this paper, we propose the concept of Suzuki type fuzzy 𝒵 -contractive mappings, which is a generalization of Fuzzy 𝒵 -contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in G -complete as well as M -complete fuzzy metric spaces. A comprehensive set of examples...

SV and related f -rings and spaces

Suzanne Larson (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

An f -ring A is an SV f -ring if for every minimal prime ℓ -ideal P of A , A / P is a valuation domain. A topological space X is an SV space if C ( X ) is an SV f -ring. SV f -rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV f -rings and spaces and on related f -rings and spaces have appeared. This article surveys what is known about these f -rings and spaces and introduces a number of new results that help to clarify the relationship between SV f -rings and spaces and related...

Swiss cheeses, rational approximation and universal plane curves

J. F. Feinstein, M. J. Heath (2010)

Studia Mathematica

We consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We develop a theory of allocation maps connected to such sets and we use this theory to modify examples previously constructed in the literature to obtain examples homeomorphic to the Sierpiński carpet. Our techniques also allow us to avoid certain technical difficulties in the literature.

Symmetric products of the Euclidean spaces and the spheres

Naotsugu Chinen (2015)

Commentationes Mathematicae Universitatis Carolinae

By F n ( X ) , n ≥ 1 , we denote the n -th symmetric product of a metric space ( X , d ) as the space of the non-empty finite subsets of X with at most n elements endowed with the Hausdorff metric d H . In this paper we shall describe that every isometry from the n -th symmetric product F n ( X ) into itself is induced by some isometry from X into itself, where X is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the n -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence and...

Szpilrajn type theorem for concentration dimension

Jozef Myjak, Tomasz Szarek (2002)

Fundamenta Mathematicae

Let X be a locally compact, separable metric space. We prove that d i m T X = i n f d i m L X ' : X ' i s h o m e o m o r p h i c t o X , where d i m L X and d i m T X stand for the concentration dimension and the topological dimension of X, respectively.

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