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Isometries of ultrametric normed spaces
We show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study...
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Isometry and phase-isometry of non-Archimedean normed spaces
In this paper, we study isometries and phase-isometries of non-Archimedean normed spaces. We show that every isometry f : S r ( X ) → S r ( X ), where X is...
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Metric Spaces
Exploring the properties of real functions or sequences is just the beginning. A few answers lead to several questions. Can we extend our results...
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A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces
We prove a very general fixed point theorem in the space of functions taking values in a random normed space (RN-space). Next, we show several of its...
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Metric Spaces
Motivates and defines the notion of metrics and metric spaces; and shows that examples of metric spaces abound in the various areas of analysis.
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Optimal embeddings for Triebel–Lizorkin and Besov spaces on quasi-metric measure spaces
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for...
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Injective Spaces
Injective hull is a useful construction that provides a canonical choice of a specially nice (injective) space that includes a given metric space....
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Basic Theory of Metric Spaces
Develops the basic machinery of metric spaces. Includes open and closed sets, convergence of sequences, continuous functions and completeness.
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Lipschitz Clustering in Metric Spaces
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces....
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Completeness of the Classical Spaces
Is devoted to proving the completeness of the important spaces of multivariate calculus and basic functional analysis.
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Topology
Consider the graphs of the capital letters of the English alphabet in a plane. By stretching and twisting, one can deform U onto S and vice versa....
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Homeomorphisms
Homeomorphisms are essentially topological isomorphisms. In other words, homeomorphic spaces are same from the topological viewpoint. In Sect. 4.4,...
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Weighted Triebel-Lizorkin and Herz Spaces Estimates for p-Adic Hausdorff Type Operator and its Applications
The aim of this paper is to establish the boundedness of the Hausdorff operator in the Triebel-Lizorkin spaces and Herz spaces with absolutely...
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An Embedding, An Extension, and An Interpolation of Ultrametrics\(^*\)
AbstractThe notion of ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove...
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Connected Spaces
Defines the notion of connected space and explores the consequences of connectedness and some of its related concepts.
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Random Processes on Non-Archimedean Spaces
The Lévy stochastic processes on p-adic numbers have been constructed by different methods. We present the construction by Albeverio and Karwowski...
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Lipschitz free p-spaces for 0 < p < 1
This paper initiates the study of the structure of a new class of p -Banach spaces, 0 < p < 1, namely the Lipschitz free p -spaces (alternatively called...