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A new inductive approach for counting dimension in large scale

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Abstract

We introduce the notion of large scale dimensiongrad as a large scale invariant of asymptotic resemblance spaces. Consequently it can be considered as a large scale invariant of metric spaces. The large scale dimensiongrad is a way of counting dimension in large scale but it is different from asymptotic dimension in general, as we show in the paper, too.

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References

  1. A. Dranishnikov, On asymptotic inductive dimension, JP J. Geom. Topol. 1 (2001), 239-247.

    MathSciNet  MATH  Google Scholar 

  2. A. Dranishnikov and M. Zarichnyi, Universal spaces for asymptotic dimension, Topol. Appl. 140 (2004) 203-225.

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Grave, Coarse geometry and asymptotic dimension, arXiv:math/0601744 (2006).

  4. M. Gromov, Asymptotic invariants of infinite groups, In: Geometric Group Theory, Vol. 2 (Sussex, 1991), 1-295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993.

  5. Sh. Kalantari and B. Honari, Asymptotic resemblance, Rocky Mountain J. Math. 46 (2016), 1231-1262.

    Article  MathSciNet  MATH  Google Scholar 

  6. Sh. Kalantar and B. Honari, On large scale inductive dimension of asymptotic resemblance spaces, Topol. Appl. 182 (2015), 107-116.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge Tract in Mathematics, No. 59, Cambridge University Press, Cambridge, London-New York, 1970.

  8. J. Roe, Lectures on Coarse Geometry, University Lecture Series, 31, American Mathematical Society, Providence, RI, 2003.

    Google Scholar 

  9. J. Smith, On asymptotic dimension of countable abelian groups, Topol. Appl. 153 (2006), 2047-2054.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Basic Sience, Babol Noshirvani University of Technology, Shariati Ave., Babol, 47148-71167, Iran

    Sh. Kalantari

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  1. Sh. Kalantari
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Correspondence to Sh. Kalantari.

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Kalantari, S. A new inductive approach for counting dimension in large scale. Arch. Math. 110, 403–412 (2018). https://doi.org/10.1007/s00013-017-1140-2

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  • DOI: https://doi.org/10.1007/s00013-017-1140-2

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