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Research topics

  • Shape thoery: various problems from ordinary shape theory, uniform shape theory, stable shape theory, strong shape theory, model category
  • Cohomological dimension and extension types
  • Shape theoretical approach to fractal geometry
  • Dimension theory for metric spaces: Assouad-Nagata dimension, asymptotic dimension, uniform dimension

Publications

reviewed by Mathematical Review and Zentralblatt

  1. T. Miyata:
    Metrization in small and large scale structures,
    Bulletin of the Polish Academy of Sciences Vol. 65 (2017).
  2. T. Miyata:
    Approximate maps characterizing injectivity and surjectivity of maps,
    Glasnik Matematicki Vol. 52 (2017), 185-203.
  3. T. Miyata:
    Factorization of uniformly continuous maps through uniform shape fibrations,
    Glasnik Matematicki Vol. 50 (2015), 233-243.
  4. T. Miyata:
    A shape theoretic approach to generalized cohomological dimension,
    Glasnik Matematicki Vol. 49 (2014), 195-220.
  5. T. Miyata:
    Normal sequences in all scales,
    Topology and its Applications Vol. 164 (2014), 146-161.
    http://dx.doi.org/doi:10.1016/j.topol.2013.12.015
  6. T. Miyata and Z. Virk:
    Dimension-raising maps in a large scale,
    Fundamenta Mathematicae Vol. 223 (2013), 83-98.
    http://dx.doi.org/doi:10.4064/fm223-1-6
  7. T. Miyata and T. Yoshimura:
    Assouad-Nagata dimension and finite-to-one Lipschitz maps,
    Topology Proceedings Vol. 42 (2013), 43-48.
  8. T. Miyata:
    Approximate extension property of mappings,
    Topology and its Applications Vol. 159 (2012), 921-932.
    http://dx.doi.org/10.1016/j.topol.2011.12.011
  9. T. Miyata:
    Homology decompositions in shape theory,
    Publicationes Mathematicae Debrecen Vol. 78 (2011), 15-35.
  10. T. Miyata:
    Strong pro-fibrations and ANR objects in pro-categories,
    Topology and its Applications Vol. 157 (2010), 2194-2224.
    http://dx.doi.org/10.1016/j.topol.2010.06.003
  11. T. Miyata:
    An approximate system approach to shape fibrations,
    Glasnik Matematicki Vol. 44 (2009), 215-240.
    http://dx.doi.org/10.3336/gm.44.1.14
  12. T. Miyata and I. Ibedou:
    The theorem of Pontrjagin and Schnirelmann and approximate resolutions,
    New Zealand Journal of Mathematics Vol. 38 (2008), 121-128.
    Abstract
  13. T. Miyata:
    Pull-backs and fibrations in approximate pro-categories,
    Glasnik Matematicki Vol. 43 (2008), 451 - 479.
    http://dx.doi.org/10.3336/gm.43.2.15
  14. T. Miyata:
    Fibrations in the category of ANR's,
    Bulletin of the Polish Academy of Sciences Mathematics Vol. 55 (2007), 145-154.
    http://dx.doi.org/10.4064/ba55-2-5
  15. T. Miyata and T. Watanabe:
    Approximate sequences and Hausdorff dimension,
    Topology Proceedings Vol. 29 (2005), 243-265.
    Abstract
  16. T. Miyata and T. Watanabe:
    An approximate system approach to box-counting dimension,
    Topology and its Applications Vol. 132 (2003), 49-69.
    http://dx.doi.org/10.1016/S0166-8641(02)00362-0
  17. T. Miyata and T. Watanabe:
    Approximate resolutions and the fractal category,
    Glasnik Matematicki Vol. 38 (2003), 377-393.
    Abstract
  18. T. Miyata and T. Watanabe:
    BiLipschitz maps and approximate resolutions,
    Glasnik Matematicki Vol. 38 (2003), 129 - 155.
    Abstract
  19. T. Miyata and T. Watanabe:
    Lipschitz functions and Approximate resolutions,
    Topology and its Applications Vol. 122 (2002), 353-375.
    http://dx.doi.org/10.1016/S0166-8641(01)00156-0
  20. T. Miyata and T. Watanabe:
    Vietoris-Begle theorem for spectral pro-homology,
    Proceedings of the American Mathematical Society Vol.130 (2002), 595-598.
    Abstract
  21. T. Miyata and T. Watanabe:
    Strong expansions for triads of spaces,
    Glasnik Matematicki Vol. 37 (2002), 147 - 161.
    Abstract
  22. T. Miyata:
    Shape aspherical compacta - applications of a theorem of Kan and Thurston to cohomological dimension and shape theories,
    Proceedings of the American Mathematical Society Vol. 129 (2001), 2783-2788.
    Abstract
  23. T. Miyata:
    $n$-shape equivalence and triads of spaces,
    Glasnik Matematicki Vol. 36 (2001), 195 - 210.
    Abstract
  24. T. Miyata and T. Watanabe:
    Approximate resolutions of uniform spaces,
    Topology and its Applications Vol. 113 (2001), 211-241.
    http://dx.doi.org/10.1016/S0166-8641(00)00011-0
  25. T. Miyata:
    Generalized stable shape and duality,
    Topology and its Applications Vol. 109 (2001), 75 - 88.
    http://dx.doi.org/10.1016/S0166-8641(99)00144-3
  26. T. Miyata:
    Moore spaces and cohomological dimension,
    Bulletin of the Polish Academy of Sciences Mathematics Vol. 48 (2000), 231 -235.
  27. T. Miyata and J. Segal:
    Generalized stable shape and Brown's representation theorem,
    Topology and its Applications Vol. 94 (1999), 275 - 305.
    http://dx.doi.org/10.1016/S0166-8641(98)00035-2
  28. T. Miyata:
    Shape theory of triads,
    Glasnik Matematicki Vol. 34 (1999), 301 - 315.
    Abstract
  29. T. Miyata:
    Uniform Vietoris-Begle theorems,
    Quaestiones Mathematicae Vol. 21 (1998), 39 - 47.
  30. T. Miyata and J. Segal:
    Shape and uniform properties of hyperspaces of noncompact spaces,
    Glasnik Matematicki Vol. 32 (1997), 99 - 124.
    Abstract
  31. T. Miyata:
    Cohomological dimension of uniform spaces,
    Quaestiones Mathematicae Vol. 19 (1996), 137 - 162.
  32. T. Miyata:
    Extension type and homology,
    Bulletin of the Polish Academy of Sciences Mathematics Vol. 44 (1996), 1 - 4.
  33. T. Miyata and J. Segal:
    Generalized stable shape and the Whitehead theorem,
    Topology and its Applications Vol. 63 (1995), 139 - 164.
    http://dx.doi.org/10.1016/0166-8641(94)00082-E
  34. T. Miyata:
    Homology, cohomology, and uniform shape,
    Glasnik Matematicki Vol. 30 (1995), 85 - 109.
  35. T. Miyata:
    Uniform shape theory,
    Glasnik Matematicki Vol. 29 (1994), 123 - 168.

Thesis paper

Geometry of uniform spaces, Ph.D Thesis, University of Washington, 1993.

Books, conference papers, and other refereed papers

  1. Progress in Mathematical Biology Research, Nova Science Publishers, Inc., 2008 (co-author).
  2. Mixed strategy for tree search, Southeastcon '89 Proceedings 'Energy and Information Technologies in the Southeast', IEEE Vol. 3, 995-998, 1989 (with S. S. Iyengar, E. Haq).
  3. Linux and its applications to education environment II, Shizuoka Institute of Technology Technical Report Vol. 8 (2000), 259 - 269 (Japanese).
  4. Linux and its applications to education environment, Shizuoka Institute of Technology Technical Report Vol. 7 (1999), 175 - 181 (Japanese).