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On the research of topological dimension of metric spaces

Research Project

Project/Area Number 09640108
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionShimane University

Principal Investigator

HATTORI Yasunao  Shimane University, Department of Mathematics and Computer Science, Professor, 総合理工学部, 教授 (20144553)

Co-Investigator(Kenkyū-buntansha) YAMADA Kohzo  Shizuoka University, Department of Mathematics, Associate Professor, 教育学部, 助教授 (00200717)
SHAKHMATOV Domitri  Ehime University, Department of Mathematics, Associate Professor, 理学部, 助教授 (90253294)
NOGURA Tsugunori  Ehime University, Department of Mathematics, Professor, 理学部, 教授 (00036419)
MAEDA Sadahiro  Shimane University, Department of Mathematics and Computer Science, Professor, 総合理工学部, 教授 (40181581)
MIWA Takuo  Shimane University, Department of Mathematics and Computer Science, Professor, 総合理工学部, 教授 (60032455)
相川 弘明  島根大学, 総合理工学部, 教授 (20137889)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordsmetric spaces / topological dimension / topological groups / finitistic spaces / K-approximation / ordered spaces / selection / complex projective plane / 連続写係 / 収束
Research Abstract

In the present research project, we investigated some dimensiontheoretic properties of metrizable spaces and its applications. Hattori considered with Yamada on two transfinite dimensions - the large transfinite dimension Ind and the order dimension O-dim - of metric spaces. They proved that for a metric space X, X has hid if and only if X has O-dim. Furthermore, the inequality Ind X < O-dim X holds. This answers the question of F.G.Arenas affirmatively. Hattori considered a convergence structure of metric groups. He proved that there is a metric group topology on the real line such that it is weaker than the usual one and the sequence {2n : n = 1, 2, ...} converges to 0. He also proved that there is no such group topology preserving the linearity. This answers the Fric's question. Yamada investigated the group structures of free groups of metrizable spaces and proved that the structures of a free group are determined by its neighborhood systems. Shakhmatov researched the topological p … More roperties of compactly generated groups and free abelian groups from dimension theoretic points of view. Hattori investigated an extension property on ordered spaces and proved that every perfect ordered space with a special condition has the Dugundji extension property. He furthered this research with G.Gruenhage and H.Ohta.Shey determined closed subspace of ordered spaces which has the Dugundji extension property. This solves the problems of Heath-Lutzer and van Douwen. Miwa considered the perfect normality and certain covering properties of ordered spaces. Nogura and Shakhmatov gave some theorems about the existence of continuous selections on the hyperspaces of metric spaces under some dimensionality conditions. Kikkawa and Maeda considered the circles in the complex projective plane. Hattori investigated metric finitistic spaces and gave a universal space theorem and a Pasynkov's type of factorization theorem for finitistic spaces. Aikawa researched the harmanic functions and measure from dimension theoretic points of view. Less

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report

Research Products

(68 results)

All Other

All Publications (68 results)

  • [Publications] Y.Hattori and K.Yamada: "Finite-to-one mappings and large transfinite dimension" Topology and its Applications. 82. 181-194 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunao Hattori: "pi-embeddings and Dugundji extension theorems for generalized ordered spaces" Topology and its Applications. 84. 43-54 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Gruenhage, Y.Hattori and Haruto Ohta: "Dugundji extenders and reteracts on generalized ordered spaces" Fundamenta Mathematicae. 158. 147-164 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunao Hattori: "Enlarging the convergence on the real line via metrizable group topology" Mathematica Slovaca. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Buhagiar and T.Miwa: "On superparacompact and Lindelof GO-spaces" Houston Journal of Mathematics. 24. 443-457 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michihiko Kikkawa: "Projectivity of Lie triple algebras" Memoirs of the Faculty of Science and Engineering, Shimane University. 31. 11-20 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Adachi, S.Maeda and Koichi Ogiu: "Extrinsic shape of circles and standard imbeddings of projective spaces" Manuscripta Mathematica. 93. 267-272 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Adachi and S.Maeda: "Length spectrum of circles in a complex projective space" Osaka Journal of Mathematics. 35. 553-565 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Kimura and S.Maeda: "Geometric meaning of isoparametric hypersurfaces in a real space form" Canadian Mathematical Bulletin. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroaki Aikawa: "Integrability of superharmonic functions in a John domain" Proc.Amer.Math.Soc.(to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Gutev and T.Nogura: "Selections for Vietoris-like hyperspace topologies" Proc.London Math.Soc. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Pestov and D.Shakhmatov: "A relatively free topological group that is not varietal free" Colloq.Math.77. 1-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Domitry Shakhmatov: "A categorical version of the Lefschets-Nobeling-Pontryagin theorem on embedding compacta in R^n" Topology Appl.85. 345-349 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Pestov and K.Yamada: "Free topological groups on metrizable spaces and inductive limits" Topology and its Applications. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kohzo Yamada: "Tightness of free abelian topological groups and of finite products of sequential fans" Topology Proceedings. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Hattori and K.Yamada: "Finite-to-one mappings and large transfinite dimension" Topology Appl.Vol.82. 181-194 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunao Hattori: "pi-embeddings and Dugundji extension theorems for generalized ordered spaces" Topology Appl.Vol.84. 43-54 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Gruenhage, Y.Hattori and H.Ohta: "Dugundji extenders and reteracts on generalized ordered spaces" Fund.Math.Vol.158. 147-164 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunao Hattori: "Enlarging the convergence on the real line via metrizable group topology" Mathematica Slovaca. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Buhagiar and T.Miwa: "On superparacompact and Lindelof GO-spaces" Houston J.Mathematics. Vol.24. 443-457 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michihiko Kikkawa: "Projectivity of Lie triple algebras" Mem.Fac.Sci.Eng.Shimane Univ.Vol.31. 11-20 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Adachi S.Maeda and K.Ogiue: "Extrinsic shape of circles and standard imbeddings of projective spaces" Manuscripta Mathematica. Vol.93. 267-272 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Adachi and S.Maeda: "Length spectrum of circles in a complex projective space" Osaka J.Mathematics. Vol.35. 553-565 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Kimura and S.Maeda: "Geometric meaning of isoparametric phypersurfaces in a real space form" Canadian Math.Bulletin. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroaki Aikawa: "Intergrability of superharmonic functions in a John domain" Proc.Amer.Math.Soc.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Gutev and T.Nogura: "Selections for Vietoris-like hyperspace topologies" Proc.London Math.Soc.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Pestov and D.Shakmatov: "A.relatively free topological group that is not varietal free" Colloq.Math.Vol.77. 1-8 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Domitry Shakmatov: "A categorical version of the Lefschets-Nobeling-Pontryagin theorem on embedding compacta in Rn" Topology Appl.Vol.85. 345-349 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] V.Pestov and K.Yamada: "Free topological groups on metrizable spaces and inductive limits" Topology Appl.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kohzo Yamada: "Tightness of free abelian topological groups and of finite products of sequential fans" Topology Proceedings. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunao Hattori: "pi-embeddings and Dugundji extension theorems for generalized ordered spaces" Topology and its Applications. 84. 43-54 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] G.Gruenhage, Y.Hattori and H.Ohta: "Dugundji extenders and reteracts on generalized ordered spaces" Fundamenta Mathematicae. 158. 147-164 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Yasunao Hattori: "Enlarging the convergence on the real line via metrizable group topology" Mathematica Slovaca. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] D.Buhagiar and T.Miwa: "On superparacompact and Lindelof Go-spaces" Houston Journal of Mathematics. 24. 443-457 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] D.Buhagiar, T.Miwa and B.Pasynkov: "On metrizable type (MT-) maps and spaces" Topology and its Applications. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] D.Buhagiar, T.Miwa and B.Pasynkov: "Superparacompact type properties" Yokohama Mathematical Journal. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Michihiko Kikkawa: "Projectivity of Lie triple algebras" Memoirs Fac.Sci.Eng.,Shimane Univ.31. 11-20 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Maeda and R.Takagi: "Cirular geodesic submanifolds with parallelmean curvature vector in a non-flat complex space form" Proc.Japan Acad.73. 55-57 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] U.Ki and S.Maeda: "Notes on extrinsic spheres" Bulletin Korean Mathematical Society. 35. 433-439 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Adachi and S.Maeda: "Length spectrum of circles in a complex projective space" Osaka Journal of Mathematics. 35. 553-565 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Kimura and S.Maeda: "Geometric meaning of isoparametric hypersurfaces in a realspace form" Canadian Mathematical Bullentin. (to appeat).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Adachi and S.Maeda: "A construction of closed helices with self-intersections in a complex projective space by using submanifold theory" Hokkaido Mathematical Journal. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Adachi, M.Kimura and S.Maeda: "A characterization of all homogeneous real hypersurfaces in a complex projective space by observing the extrinsic shape of geodesics" Archiv der Mathematik. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Adachi and S.Maeda: "Circular helices in a standard sphere" New Zealand Mathematical Journal. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Aikawa: "Capacity and Hausdorff content of certain enlarged sets" Mem.Fac.Sci.Eng.Shimane Univ.30. 1-21 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Aikawa: "Densities with the mean value property for harmonic functions in a Lipschitz domain" Proc.Amer.Math.Soc.125. 229-234 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Aikawa: "Generalized Cranston-McConnell inequalities for discontinuous superhamonic functions" Potential Analysis. 8. 127-135 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Aikawa: "Norm estimate for the Green operator with applications" Proc.Conference in honor of Matis Essen. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Aikawa: "Integrability of superharmonic functions in a John domain" Proc.Amer.Math.Soc.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Fric and T.Nogura: "Rings of maps : Sequential convrgence and completion and strictness" Tatra Mt.Math.Publ.14. 137-143 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.V.Arhangel'skii, T.Nogura: "Relative sequentiality" Topology Appl.82. 49-58 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] V.Gutev and T.Nogura: "Selections for Vietoris-like hyperspace topologies" Proc.London Math.Soc.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Dolecki and T.Nogura: "Two-fold theorem on Frechetness of products" Czech.MAth.J.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] V.Pestov and D.Shakmatov: "A relatively free topological group that is not varietal free" Colloq.Math.77. 1-8 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Domitry Shakmatov: "A categorical version of the Lefschets-Nobeling-Pontryagin theorem on embedding compacta in R^n" Topology Appl.85. 345-349 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Ohta and K.Yamada: "On spaces with linearly homeomorphic function spaces in the compact open topology" Tsukuba Journal of Mathematics. 22. 39-48 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Hattori & K.Yamada: "Finite-to-one mappings and large transfinite dimension" Topology and Its Applications. 82. 181-194 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Hattori: "Enlarging the convergence on the real line via metrizable group topologies" Math.Slovaca. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Hattori: "Tv-embeddings and Dugundji extension thorems for generalized ordered spaces" Topology and its Applications. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Yamada: "Tightness of free topological groups and of finite products of sequential fans" Topology Proceedings. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Ohta & K.Yamada: "Simple examples showing that various topological properties are not finitely additive in the sense of V.V.Tkachuk" Math,Japonioca. 47. 93-95 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] V.Pestov & K.Yamada: "Free topological groups on metrizable spaces and inductive limits" Topology and its Applications. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Nogura & D.Shakhmatov: "Characterizations of intervals via continuous selections" Circolo Math.Di.Palermo. 46. 317-328 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Nogura & D.Shakhmatov: "Spaces which have finitely many continuous selections" Unione Mathematica Italiana. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Adachi & S.Maeda: "Holomorphic helices in a complex space form" Proc.Amer.Math.Soc.125. 1197-1202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Maeda & K.Ogiue: "Characterization of geodesic hyperspheres in a complex projective space by observing the extrinsic shape of geodesics" Math.Z.225. 537-542 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Adachi,S.Maeda & K.Ogiue: "Extrinsic shape of circles and standard imbeddin of projective spaces." Manuscripta Math.93. 267-272 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] D.Buhagiar & T.Miwa: "Ordered uniform completions of GO-spaces" Topology Proceedings. (to appear).

    • Related Report
      1997 Annual Research Report

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Published: 1997-03-31   Modified: 2016-04-21  

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