研究者紹介システム

宮田 任寿
ミヤタ タカヒサ
大学院人間発達環境学研究科 人間環境学専攻
教授
数学関係
Last Updated :2022/04/15

研究者情報

所属

  • 【主配置】

    大学院人間発達環境学研究科 人間環境学専攻
  • 【配置】

    国際人間科学部 環境共生学科, 発達科学部 人間環境学科

学位

  • Ph.D., ワシントン大学

授業科目

ジャンル

  • 科学・技術 / 数学

コメントテーマ

  • 幾何学的トポロジー

研究活動

研究キーワード

  • トポロジー,shape理論とその応用

研究分野

  • 自然科学一般 / 幾何学

論文

  • Metrization in small and large scale structures

    宮田 任寿

    2017年, Bulletin of the Polish Academy of Sciences, 65, 81 - 92, 英語

    [査読有り][招待有り]

    研究論文(学術雑誌)

  • APPROXIMATE MAPS CHARACTERIZ INGINJECTIVITY AND SURJECTIVITY OF MAPS

    Takahisa Miyata

    In the theory of inverse systems, in order to study the properties of a space X or a map f: X -> Y between spaces, one expands X to an inverse system X or expands f to a map f: X -> Y between the inverse systems, and then work on X or f. In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f: X -> Y between compact metric spaces is injective (resp., surjective) if and only if any approximate map f : X ->(sic) whose limit is f is injective (resp., surjective). As a consequence, we show that an approximate map f : X -> (sic) is approximately injective (resp., approxim ately surjective) if and only if f represents a monomorphism( resp., an epimorphism)in the approximate pro-category in the sense of Mardesic and Watanabe.

    CROATIAN MATHEMATICAL SOC, 2017年, GLASNIK MATEMATICKI, 52 (1), 185 - 203, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Factorization of uniformly continuous maps through uniform shape fibrations

    宮田 任寿

    Croatian Mathematical Society and University of Zagreb, 2015年06月, Glasnik Matematicki, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Takahisa Miyata

    The metrization theorem of Alexandroff and Urysohn is known as a strong tool in general topology. In this paper, using the notion of Alexandroff and Urysohn metric, we introduce the notions of all-scale normal sequence, large-scale normal sequence, and small-scale normal sequence to establish a new unified approach to study various concepts of metric geometry in all scales. This approach provides us with the interplay between topology and metric geometry. We show that all-scale, large-scale, and small-scale concepts of metric spaces can be studied as topological problems, using the notions of normal sequences in appropriate scales. The concepts which we deal with are metrization, Lipschitz category, the Assouad-Nagata dimension as an all-scale concept; the uniform category, the topological category, the uniform dimension, the covering dimension as a small-scale concept; the coarse category, large-scale Lipschitz maps, quasi-isometric maps, the asymptotic dimension, and the asymptotic Assouad-Nagata dimension as a large-scale concept. This approach also provides us with the interplay between various concepts of metric geometry in different scales. As an application, we obtain some relations of the Assouad Nagata dimension to the uniform dimension, the covering dimension, and the asymptotic dimension. (C) 2013 Elsevier B.V. All rights reserved.

    ELSEVIER SCIENCE BV, 2014年03月, TOPOLOGY AND ITS APPLICATIONS, 164 (1), 146 - 161, 英語

    [査読有り]

    研究論文(学術雑誌)

  • A SHAPE THEORETIC APPROACH TO GENERALIZED COHOMOLOGICAL DIMENSION WITH RESPECT TO TOPOLOGICAL SPACES

    Takahisa Miyata

    A. N. Dranishnikov introduced the notion of generalized cohomological dimension of compact metric spaces with respect to CW spectra. In this paper, taking an inverse system approach, we generalize this definition and obtain two types of generalized comological dimension with respect to general topological spaces, which are objects in the stable shape category. We characterize those two types of generalized cohomological dimension in terms of maps and obtain their fundamental properties. In particular, we obtain their relations to the integral cohomological dimension and the covering dimension. Moreover, we study the generalized cohomological dimensions of compact Hausdorff spaces with respect to the Kahn continuum and the Hawaiian earing.

    CROATIAN MATHEMATICAL SOC, 2014年, GLASNIK MATEMATICKI, 49 (1), 195 - 220, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Assouad-Nagata dimension and finite-to-one Lipschitz maps

    Takahisa Miyata, Takehiro Yoshimura

    2013年06月, Topology Proceedings, Vol. 42, 43-48, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Takahisa Miyata, Ziga Virk

    Hurewicz's dimension-raising theorem states that dim Y <= dim X + n for every n-to-1 map f : X -> Y. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a dimension-raising type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension. It is also well-known (Hurewicz's finite-to-one mapping theorem) that dim X <= n if and only if there exists an (n 1)-to-1 map from a 0-dimensional space onto X. We formulate a finite-to-one mapping type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension.

    POLISH ACAD SCIENCES INST MATHEMATICS, 2013年, FUNDAMENTA MATHEMATICAE, 223 (1), 83 - 97, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Approximate extension property of mappings

    Takahisa Miyata

    2012年01月, Topology and its Applications, 159・3・921-932, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Takahisa Miyata

    In this paper, for each inverse sequence G of abelian groups and for each n > 1, we introduce the notion of approximate Moore space of type (G, n) and obtain shape theoretical homology decompositions for metric continua in the sense of E. H. Brown and A. H. Copeland.

    KOSSUTH LAJOS TUDOMANYEGYETEM, 2011年01月, PUBLICATIONES MATHEMATICAE-DEBRECEN, 78 (1), 15 - 35, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Takahisa Miyata

    The notions of pro-fibranon and approximate pro-fibration for morphisms in the procategory pro-Top of topological spaces were introduced by S Mardesic and T.B Rushing In this paper we introduce the notion of strong pro-fibration, which is a pro-fibranon with some additional property, and the notion of ANR object in pro-Top, which is approximately an ANR-system, and we consider the full subcategory ANR of pro-Top whose objects are ANR objects We prove that the category ANR. satisfies most of the axioms for fibration category in the sense of H.J Baues if fibrations are strong pro-fibranons and weak equivalences are morphisms inducing isomorphisms in the pro-homotopy category pro-H(Top) of topological spaces. We give various applications. First of all, we prove that every shape morphism is represented by a strong pro-fibration Secondly, the fibre of a strong pro-fibration is well defined in the category ANR, and we obtain an isomorphism between the pro-homotopy groups of the base and total systems of a strong pro-fibration, and hence obtain the pro-homotopy sequence of a strong pro-fibration. Finally, we also show that there is a homotopy decomposition in the category ANR. (C) 2010 Elsevier BV All rights reserved

    ELSEVIER SCIENCE BV, 2010年09月, TOPOLOGY AND ITS APPLICATIONS, 157 (14), 2194 - 2224, 英語

    [査読有り]

    研究論文(学術雑誌)

  • An approximate system approach to shape fibrations

    Takahisa Miyata

    2009年, Glasnik Matematicki, Vol. 44, 215-240

    [査読有り]

    研究論文(学術雑誌)

  • The theorem of Pontrjagin and Schnirelmann and approximate resolutions

    Takahisa Miyata

    2008年, New Zealand Journal of Mathematics, Vol. 38, 121-128

    [査読有り]

    研究論文(学術雑誌)

  • Pull-backs and fibrations in approximate pro-categories

    Takahisa Miyata

    2008年, Glasnik Matematicki, vol. 43 (2008), 451 - 479

    [査読有り]

    研究論文(学術雑誌)

  • Fibrations in the category of ANR's

    Takahisa Miyata

    2007年, Bulletin of the Polish Academy of Sciences, 55

    [査読有り]

    研究論文(学術雑誌)

  • Approximate sequences and Hausdorff dimension

    Takahisa Miyata, Tadashi Watanabe

    In this paper, we introduce a new approach using normal sequences and approximate sequences to study Hausdorff dimension for compact metrizable spaces. Using this approach, for each r > 0, we construct a Cantor set X, with Hausdorff dimension r in the cube [0, 1](N), where N is the least integer that is greater than or equal to log3/log2(r + 1) + 1.

    AUBURN UNIV, 2005年, Topology Proceedings, Vol 29, No 1, 2005, 29 (1), 243 - 265, 英語

    [査読有り]

    研究論文(国際会議プロシーディングス)

  • T Miyata, T Watanabe

    In an earlier paper the authors introduced a new approach using normal sequences and approximate resolutions to study Lipschitz maps between compact metric spaces. In this paper we introduce two kinds of box-counting dimension, which are defined for every compact metric space with a normal sequence and for every approximate resolution of any compact metric space, and investigate their properties. In a special case those notions coincide with the usual box-counting dimension for compact subsets of R-n. Our box-counting dimensions are Lipschitz subinvariant, where Lipschitz maps are in the sense of the earlier paper. Moreover, we obtain fundamental theorems such as the subset theorem, the product theorem and the sum theorem. As an example, for each r with 0 less than or equal to r less than or equal to infinity, we present a systematic way to construct a compact metric space with an approximate resolution whose box-counting dimension equals r. (C) 2002 Elsevier B.V. All rights reserved.

    ELSEVIER SCIENCE BV, 2003年07月, TOPOLOGY AND ITS APPLICATIONS, 132 (1), 49 - 69, 英語

    [査読有り]

    研究論文(学術雑誌)

  • BiLipschitz maps and approximate resolutions

    Miyata Takahisa, Watanabe Tadashi

    2003年, Glasnik Matematicki, 38, 129-155, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Approximate resolutions and the fractal category

    Miyata Takahisa, Watanabe Tadashi

    2003年, Glasnik Matematicki, 38, 377-393, 英語

    [査読有り]

    研究論文(学術雑誌)

  • An approximate system approach to box-counting dimension

    Miyata Takahisa, Watanabe Tadashi

    2003年, Topology and its Applications, 132, 49-69, 英語

    [査読有り]

    研究論文(学術雑誌)

  • T Miyata, T Watanabe

    A Lipschitz function between metric spaces is an important notion in fractal geometry as it is well known to have a close connection to fractal dimension. On the other hand, the theory of approximate resolutions has been developed by Mardesic and Watanabe. In this theory maps f : X --> Y between general spaces are represented by approximate maps f : X Y between approximate systems for any approximate resolutions p: X --> X and q : Y --> Y, and the approximate maps f give useful information about the properties of the maps f. In this paper, we describe a new method of using the theory of approximate resolutions to study Lipschitz functions. More precisely, first of all, given a Hausdorff space X and a normal sequence U with a reasonable condition, a new metric d(U) which induces the given topology is defined, and Lipschitz functions with respect to the metrics induced by normal sequences are characterized by a property of the normal sequences. Secondly, using this metric, for each compact metric space X and for each approximate resolution p: X --> X of X with a reasonable condition, a new metric d(p) which is topologically equivalent to the given metric is defined, and the properties of those metrics are investigated. Lipschitz functions between continua with the metrics induced by approximate resolutions are characterized by approximate resolutions. As an application, contraction maps are characterized, and a sufficient condition in terms of approximate resolutions for the existence of a unique fixed point is obtained. (C) 2002 Elsevier Science B.V. All rights reserved.

    ELSEVIER SCIENCE BV, 2002年07月, TOPOLOGY AND ITS APPLICATIONS, 122 (1-2), 353 - 375, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Strong expansions for triads of spaces

    Miyata Takahisa, Watanabe Tadashi

    2002年, Glasnik Matematicki, 37, 147 - 161, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Shape aspherical compacta - applications of a theorem of Kan and Thurston to cohomological dimension and shape theories

    Miyata Takahisa

    2001年, Proceedings of the American Mathematical Society, 129, 2783-2788, 英語

    [査読有り]

    研究論文(学術雑誌)

  • n-shape equivalence and triads of spaces

    Miyata Takahisa

    2001年, Glasnik Matematicki, 36, 195 - 210, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Generalized stable shape and duality

    Miyata Takahisa

    2001年, Topology and its Applications, 109, 75 - 88, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Approximate resolutions of uniform spaces

    Miyata Takahisa, Watanabe Tadashi

    2001年, Topology and its Applications, 113, 211-241, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Approximate resolutions and fractal geometry

    Miyata Takahisa, Watanabe Tadashi

    2001年, RIMS Kokyuroku, 1248, 24-31, 英語

    研究論文(国際会議プロシーディングス)

  • Vietoris-Begle theorem for spectral pro-homology

    T Miyata, T Watanabe

    Dydak and Kozlowski (1991) obtained a generalization of the Vietoris-Begle theorem for the cohomology theories induced by CW spectra. In this note we prove a dual of their theorem involving the pro-homology theories induced by CW spectra.

    AMER MATHEMATICAL SOC, 2001年, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 130 (2), 595 - 598, 英語

    [査読有り]

    研究論文(学術雑誌)

  • On shape theory and its applications

    Miyata Takahisa

    2000年, RIMS Kokyuroku, 1188, 46-54, 英語

    研究論文(国際会議プロシーディングス)

  • Moore spaces and cohomological dimension

    Miyata Takahisa

    2000年, Bulletin of the Polish Academy of Sciences, 48, 231 -235, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Linuxを利用した教育環境 Ⅱ - phpとPostgreSQLの利用

    宮田 任寿

    2000年, 静岡理工科大学紀要, 8, 259-269, 日本語

    [査読有り]

    研究論文(学術雑誌)

  • Generalized stable shape and Brown's representation theorem

    T Miyata, J Segal

    In this paper we formulate and prove the absolute and relative versions of the Hurewicz theorem and the homological version of the Whitehead theorem in the generalized stable shape category. We also apply Brown's representation theorem to obtain various properties of generalized stable shape and shape. (C) 1999 Elsevier Science B.V. All rights reserved.

    ELSEVIER SCIENCE BV, 1999年06月, TOPOLOGY AND ITS APPLICATIONS, 94 (1-3), 275 - 305, 英語

    研究論文(学術雑誌)

  • Generalized stable shape and Brown's representation theorem

    T Miyata, J Segal

    In this paper we formulate and prove the absolute and relative versions of the Hurewicz theorem and the homological version of the Whitehead theorem in the generalized stable shape category. We also apply Brown's representation theorem to obtain various properties of generalized stable shape and shape. (C) 1999 Elsevier Science B.V. All rights reserved.

    ELSEVIER SCIENCE BV, 1999年06月, TOPOLOGY AND ITS APPLICATIONS, 94 (1-3), 275 - 305, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Shape theory of triads

    Miyata Takahisa

    1999年, Glasnik Matematicki, 34, 301-315, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Linuxを利用した教育環境

    宮田 任寿

    1999年, 静岡理工科大学紀要, 7, 175-181, 日本語

    [査読有り]

    研究論文(学術雑誌)

  • Uniform Vietoris-Begle theorems

    Miyata Takahisa

    1998年, Quaestiones Mathematicae, 21, 39 - 47, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Approximate resolutions of uniform spaces

    Miyata Takahisa, Watanabe Tadashi

    1998年, General Topology Symposium, , 83-89, 英語

    研究論文(国際会議プロシーディングス)

  • Shape and uniform properties of hyperspaces of noncompact spaces

    Miyata Takahisa, Segal Jack

    1997年, Glasnik Matematicki, 32, 99 - 124, 英語

    [査読有り]

    研究論文(学術雑誌)

  • On hyperspaces of noncompact spaces

    Miyata Takahisa, Segal Jack

    1996年, 沼津高専研究報告書, 31, 49-56, 英語

    研究論文(学術雑誌)

  • Extension type and homology

    Miyata Takahisa

    1996年, Bulletin of the Polish Academy of Sciences, 44, 1-4, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Cohomological dimension of uniform spaces

    Miyata Takahisa

    1996年, Quaestiones Mathematicae, 19, 137 - 162, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Homology, cohomology, and uniform shape

    Takahisa Miyata

    1995年, Glasnik Matematicki, Vol. 30, 85 - 109

    [査読有り]

    研究論文(学術雑誌)

  • Generalized stable shape and the Whitehead theorem

    Takahisa Miyata, Jack Segal

    1995年, Topology and its Applications, Vol 63, 139 - 164

    [査読有り]

    研究論文(学術雑誌)

  • Uniform shape theory

    Takahisa Miyata

    1994年, Glasnik Matematicki, Vol. 29, 123 - 168

    [査読有り]

    研究論文(学術雑誌)

  • Mixed strategy for tree search

    Takahisa Miyata, S. S. Iyengar, E. Haq

    1989年, Southeastcon '89 Proceedings 'Energy and Information Technologies in the Southeast', IEEE, Vol. 3, 995-998

    [査読有り]

    研究論文(学術雑誌)

MISC

  • 手で触る数理情報教育

    宮田 任寿, 長坂 耕作, 高橋 正

    2007年03月, 神戸大学発達科学部研究紀要, 第14巻,第2号, 日本語

    速報,短報,研究ノート等(学術雑誌)

  • Extension property and cohomological dimension

    Takahisa Miyata

    1995年, General Topology Symposium, 49 - 55

    速報,短報,研究ノート等(学術雑誌)

  • Classifying spaces for dimension and extension property

    Takahisa Miyata

    1995年, 沼津高専研究報告書, Vol. 30, 83 - 86

    速報,短報,研究ノート等(学術雑誌)

書籍等出版物

  • Progress in Mathematical Biology Research

    Takahisa Miyata

    共著, Nova Science Publishers, Inc., 2008年09月, 英語

    学術書

  • キーワード 人間と発達[増補改訂版] V. 生活とテクノロジー

    丸谷 宣子, 井上 真理, 青木 務, 平山 洋介, 市橋 秀樹, 浜口 八朗, 高橋 正, 長坂 耕作, 矢野 澄雄, 福田 博也, 城 仁士, 阪本 雄二, 高橋 譲嗣, 高橋 真, 白倉 暉弘, 稲葉 太一, 白杉 直子, 近江戸 伸子, 宮田 任寿, 澤 宗則, 二宮 厚美

    共著, 大学教育出版, 2007年04月, 日本語

    教科書・概説・概論

講演・口頭発表等

  • Approximate resolutions and fractal geometry

    Miyata Takahisa

    Osaka Meeting on Geometric Topology, 2002年07月, 英語, 大阪, 日本, 国際会議

    口頭発表(招待・特別)

  • Approximate resolutions and Hausdorff dimension

    Miyata Takahisa

    International Conference on Topology and its Applications, joined with the Second Japan-Mexico Topology Symposium (Topology in Matsue), 2002年06月, 英語, 日本数学会, 島根大学, 松江, 日本, 国際会議

    口頭発表(招待・特別)

  • Lipschitz maps and approximate resolutions

    Miyata Takahisa

    一般・幾何学的トポロジーとその応用に関する研究集会, 2001年10月, 英語, 京都大学数理解析研究所, 京都, 日本, 国内会議

    口頭発表(招待・特別)

  • On shape theory and its applications

    Miyata Takahisa

    集合論的・幾何学的トポロジーとその応用に関する研究集会, 2000年10月, 日本語, 京都大学数理解析研究所, 京都, 日本, 国内会議

    口頭発表(招待・特別)

  • Shape theory from the viewpoint of homotopy theory

    Miyata Takahisa

    International Conference on Topology and its Applications, 1999年07月, 英語, 神奈川大学, 横浜, 日本, 国際会議

    口頭発表(一般)

  • Approximate resolutions of uniform spaces

    Miyata Takahisa, Watanabe Tadashi

    International Conference on Geometric Topology, 1998年10月, 英語, University of Zagreb, Dubrovnik, Croatia, 国際会議

    口頭発表(一般)

  • Stable shape and Brown's representation theorem

    Miyata Takahisa

    一般及び幾何学的トポロジー研究集会, 1998年03月, 日本語, 京都大学数理解析研究所, 京都, 日本, 国内会議

    口頭発表(招待・特別)

所属学協会

  • American Mathematical Society

共同研究・競争的資金等の研究課題