{"title":"Metric spaces with asymptotic property C and finite decomposition complexity","authors":"Jingming Zhu, WU Yan, J. Zhu, WU Y.","doi":"10.23952/jnfa.2021.15","DOIUrl":null,"url":null,"abstract":"We construct a class of metric spaces Xω+k whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω+k for any k ∈N, where ω is the smallest infinite ordinal number and a metric space Y2ω whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces Xω+k and Y2ω have finite decomposition complexity.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2021.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We construct a class of metric spaces Xω+k whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω+k for any k ∈N, where ω is the smallest infinite ordinal number and a metric space Y2ω whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces Xω+k and Y2ω have finite decomposition complexity.
期刊介绍：
Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.
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