The Experts below are selected from a list of 4317 Experts worldwide ranked by ideXlab platform
Jingming Zhu - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic property C of the wreath product ZwrZ.
arXiv: Group Theory, 2020Co-Authors: Jingming ZhuAbstract:Using the relationship between Transfinite asymptotic dimension and asymptotic property C, we obtain that the wreath product Z wr Z has asymptotic property C. Specifically, we prove that the Transfinite asymptotic dimension of the wreath product Z wr Z is no more than omega+ 1.
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a metric space with its Transfinite asymptotic dimension ω 1
Topology and its Applications, 2020Co-Authors: Jingming ZhuAbstract:Abstract We construct a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω + 1 , where ω is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not true.
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examples of metric spaces with asymptotic property c
arXiv: Functional Analysis, 2019Co-Authors: Jingming ZhuAbstract:We construct a class of metric spaces whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2\omega$. Moreover, we study the relationship between asymptotic dimension growth, Transfinite asymptotic dimension and finite decomposition complexity.
James D. Louck - One of the best experts on this subject based on the ideXlab platform.
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Transfinite Function Iteration and Surreal Numbers
Advances in Applied Mathematics, 1997Co-Authors: W.a. Beyer, James D. LouckAbstract:AbstractLouck has developed a relation between surreal numbers up to the first Transfinite ordinal ω and aspects of iterated trapezoid maps. In this paper, we present a simple connection between Transfinite iterates of the inverse of the tent map and the class of all the surreal numbers. This connection extends Louck's work to all surreal numbers. In particular, one can define the arithmetic operations of addition, multiplication, division, square roots, etc., of Transfinite iterates by conversion of them to surreal numbers. The extension is done by Transfinite induction. Inverses of other unimodal onto maps of a real interval could be considered and then the possibility exists of obtaining different structures for surreal numbers
Zhu Jingming - One of the best experts on this subject based on the ideXlab platform.
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On metric spaces with given Transfinite asymptotic dimensions
2020Co-Authors: Wu Yan, Zhu Jingming, Radul TarasAbstract:For every countable ordinal number $\xi$, we construct a metric space $X_{\xi}$ whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\xi$. We also prove that the metric space $X_{\xi}$ has finite decomposition complexity.Comment: 18 page
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Examples of metric spaces with asymptotic property $C$
2020Co-Authors: Wu Yan, Zhu JingmingAbstract:We construct a class of metric spaces whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2\omega$. Moreover, we study the relationship between asymptotic dimension growth, Transfinite asymptotic dimension and finite decomposition complexity.Comment: arXiv admin note: text overlap with arXiv:1908.0043
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A metric space with its Transfinite asymptotic dimension omega + 1
2019Co-Authors: Wu Yan, Zhu JingmingAbstract:We construct a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both omega+1, where omega is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not true
Wu Yan - One of the best experts on this subject based on the ideXlab platform.
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On metric spaces with given Transfinite asymptotic dimensions
2020Co-Authors: Wu Yan, Zhu Jingming, Radul TarasAbstract:For every countable ordinal number $\xi$, we construct a metric space $X_{\xi}$ whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\xi$. We also prove that the metric space $X_{\xi}$ has finite decomposition complexity.Comment: 18 page
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Examples of metric spaces with asymptotic property $C$
2020Co-Authors: Wu Yan, Zhu JingmingAbstract:We construct a class of metric spaces whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2\omega$. Moreover, we study the relationship between asymptotic dimension growth, Transfinite asymptotic dimension and finite decomposition complexity.Comment: arXiv admin note: text overlap with arXiv:1908.0043
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A metric space with its Transfinite asymptotic dimension omega + 1
2019Co-Authors: Wu Yan, Zhu JingmingAbstract:We construct a metric space whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both omega+1, where omega is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not true
Radul Taras - One of the best experts on this subject based on the ideXlab platform.
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On metric spaces with given Transfinite asymptotic dimensions
2020Co-Authors: Wu Yan, Zhu Jingming, Radul TarasAbstract:For every countable ordinal number $\xi$, we construct a metric space $X_{\xi}$ whose Transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\xi$. We also prove that the metric space $X_{\xi}$ has finite decomposition complexity.Comment: 18 page
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A metric space with Transfinite asymptotic dimension $2\omega$
2020Co-Authors: Radul TarasAbstract:We build an example of a metric space with Transfinite asymptotic dimension $2\omega$
