Property A and coarse embeddability for fuzzy metric spaces

We define property A for fuzzy metric spaces in the sense of George and Veeramani, show that it is an invariant in the coarse category of fuzzy metric spaces, and provide characterizations of it for uniformly locally finite fuzzy metric spaces. We also show that uniformly locally finite fuzzy metric spaces with property A are coarsely embeddable into Hilbert space.

[1]  Nebojša M. Ralević,et al.  Fuzzy metric and its applications in removing the image noise , 2019, Soft Comput..

[2]  Guoliang Yu.  Baum-Connes conjecture and coarse geometry , 1995 .

[3]  M. Ostrovskii.  Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces , 2013 .

[4]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[5]  Samuel Morillas,et al.  Examples of fuzzy metrics and applications , 2011, Fuzzy Sets Syst..

[6]  Ivan Kramosil,et al.  Fuzzy metrics and statistical metric spaces , 1975, Kybernetika.

[7]  Pawel Grzegrzolka.  Asymptotic dimension of fuzzy metric spaces , 2020, Fuzzy Sets Syst..

[8]  N. Higson,et al.  Amenable group actions and the Novikov conjecture , 2000 .

[9]  John Roe,et al.  Index theory, coarse geometry, and topology of manifolds , 1996 .

[10]  Hiroki Sako.  Property A and the operator norm localization property for discrete metric spaces , 2014 .

[11]  Hiroki Sako.  Property A for coarse spaces , 2013, Topology and its Applications.

[12]  Nilufer Koldan,et al.  Index Theory , 2004 .

[13]  Coarse Non-Amenability and Coarse Embeddings , 2011, 1101.1993.

[14]  John Roe,et al.  Lectures on coarse geometry , 2003 .

[15]  M. Menger,et al.  Ensembles flous et fonctions aléatoires , 2003 .

[16]  Guoliang Yu,et al.  The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space , 2000 .

[17]  V. H. Badshah,et al.  On Some Results in Fuzzy Metric Spaces , 2014 .

[18]  Groups with a Polynomial Dimension Growth , 2004, math/0405239.

[19]  M. Gromov.  Groups of polynomial growth and expanding maps , 1981 .

[20]  Property A and asymptotic dimension , 2008 .

[21]  Mathématiques DE L’I.H.É.S,et al.  Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms , 1968 .

[22]  B. Schweizer,et al.  Statistical metric spaces. , 1960 .

[23]  Xuegang Luo,et al.  Image Denoising via Fast and Fuzzy Non-local Means Algorithm , 2019, J. Inf. Process. Syst..

[24]  Some notes on Property A , 2006, math/0612492.

[25]  Guoliang Yu.  The Novikov conjecture for groups with finite asymptotic dimension , 1998 .

[26]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[27]  K Menger.  Probabilistic Theories of Relations. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Mariusz Grabiec,et al.  Fixed points in fuzzy metric spaces , 1988 .

[29]  K. Menger.  Statistical Metrics. , 1942, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[31]  Narutaka Ozawa.  Metric Spaces with Subexponential asymptotic Dimension Growth , 2012, Int. J. Algebra Comput..

[32]  K Menger,et al.  Probabilistic Geometry. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Bounded Geometry and Property A for Nonmetrizable Coarse Spaces , 2011 .