Ultradiversification of Diversities

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI:10.1515/agms-2020-0100

Pouya Haghmaram, K. Nourouzi

引用次数: 0

Abstract

Abstract In this paper, using the idea of ultrametrization of metric spaces we introduce ultradiversification of diversities. We show that every diversity has an ultradiversification which is the greatest nonexpansive ultra-diversity image of it. We also investigate a Hausdorff-Bayod type problem in the setting of diversities, namely, determining what diversities admit a subdominant ultradiversity. This gives a description of all diversities which can be mapped onto ultradiversities by an injective nonexpansive map. The given results generalize similar results in the setting of metric spaces.

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多样性的超多样化

摘要本文利用度量空间的超度量化思想，引入了分集的超度量化。我们发现每一种多样性都有一个超多样性，这是它最大的非膨胀超多样性图像。我们还研究了多样性设置中的Hausdorff-Bayod型问题，即确定哪些多样性允许亚显性超多样性。这给出了所有能被一个内射非膨胀映射映射到超多样性上的多样性的描述。给出的结果推广了度量空间中类似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.