1998 Fiscal Year Annual Research Report

距離空間における位相次元の研究

Research Project

Project/Area Number	09640108
Research Institution	Shimane University
Principal Investigator	服部泰直島根大学, 総合理工学部, 教授 (20144553)
Co-Investigator(Kenkyū-buntansha)	ドミトリーシャクマトラ愛媛大学, 理学部, 助教授 (90253294) 野倉嗣紀愛媛大学, 理学部, 教授 (00036419) 相川弘明島根大学, 総合理工学部, 教授 (20137889) 前田定廣島根大学, 総合理工学部, 教授 (40181581) 三輪拓夫島根大学, 総合理工学部, 教授 (60032455)
Keywords	距離空間 / 位相次元 / 位相群 / finitistic spaces / K-近似 / 順序空間 / 選択関数 / 複素射影空間
Research Abstract	次元論における話題としてfinitistic spacesの理論がある。Finitistic spacesは、コンパクト空間と有限次元空間に共通する一般化として1960年にSwanにより導入された。そして、finitistic spacesは、不動点理論及び変換群にコホモロジー的観点からの応用を与えた。次元論におけるfinitistic spacesの特性を研究する立場に立ち、服部は距離空間おけるfinitistic spacesの万有空間の存在を証明した。これは、服部が1985年に提起した問題を肯定的な解である。また、finitistic spacesに対するPasynkovのタイプのfactorization theoremが成り立つことを示した。上の結果に関連して、最近Dydak-Mishra-Shuklaによって開発されたK-近似理論を使い、強可算次元空間の特性化定理を得た。これらの結果は、現在発表するための準備を進めているところである。三輪は、順序空間に関する前年度の研究をさらに進め、順序空間におけるいくつかの被覆定理を得た。これらは、順序空間における位相次元を調べる上で有用である。また、順序空間とファイバーワイズ・トポロジーとの関連についても研究した。吉川と前田は、位相次元に関する微分幾何学的側面の研究を行い、特に吉川は、リー代数系における幾何学的性質を、そして前田は、主に複素射影空間内における曲線(円)の性質と位相次元との関連について調べた。相川は、調和関数と測度そして位相次元との関連について研究した。野倉は、収束構造と位相的性質の関連を調べ、距離空間の超空間上における連続な選択関数の存在性を位相次元との関連から調べた。Shakhmatovは、次元論において古典的な定理であるコンパクト距離空間に対するLefschets-Nobeling-Pontryaginの埋め込み定理のカテゴリカルな観点からの見直しを行った。また、コンパクト生成な距離位相群や、自由アーベル位相群における位相的性質を次元論の観点から調べた。

Research Products
(26 results)

All Other

All Publications (26 results)

[Publications] Yasunao Hattori: "pi-embeddings and Dugundji extension theorems for generalized ordered spaces" Topology and its Applications. 84. 43-54 (1998)
[Publications] G.Gruenhage, Y.Hattori and H.Ohta: "Dugundji extenders and reteracts on generalized ordered spaces" Fundamenta Mathematicae. 158. 147-164 (1998)
[Publications] Yasunao Hattori: "Enlarging the convergence on the real line via metrizable group topology" Mathematica Slovaca. (to appear).
[Publications] D.Buhagiar and T.Miwa: "On superparacompact and Lindelof Go-spaces" Houston Journal of Mathematics. 24. 443-457 (1998)
[Publications] D.Buhagiar, T.Miwa and B.Pasynkov: "On metrizable type (MT-) maps and spaces" Topology and its Applications. (to appear).
[Publications] D.Buhagiar, T.Miwa and B.Pasynkov: "Superparacompact type properties" Yokohama Mathematical Journal. (to appear).
[Publications] Michihiko Kikkawa: "Projectivity of Lie triple algebras" Memoirs Fac.Sci.Eng.,Shimane Univ.31. 11-20 (1998)
[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)
[Publications] U.Ki and S.Maeda: "Notes on extrinsic spheres" Bulletin Korean Mathematical Society. 35. 433-439 (1998)
[Publications] T.Adachi and S.Maeda: "Length spectrum of circles in a complex projective space" Osaka Journal of Mathematics. 35. 553-565 (1998)
[Publications] M.Kimura and S.Maeda: "Geometric meaning of isoparametric hypersurfaces in a realspace form" Canadian Mathematical Bullentin. (to appeat).
[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).
[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).
[Publications] T.Adachi and S.Maeda: "Circular helices in a standard sphere" New Zealand Mathematical Journal. (to appear).
[Publications] Hiroaki Aikawa: "Capacity and Hausdorff content of certain enlarged sets" Mem.Fac.Sci.Eng.Shimane Univ.30. 1-21 (1997)
[Publications] Hiroaki Aikawa: "Densities with the mean value property for harmonic functions in a Lipschitz domain" Proc.Amer.Math.Soc.125. 229-234 (1997)
[Publications] Hiroaki Aikawa: "Generalized Cranston-McConnell inequalities for discontinuous superhamonic functions" Potential Analysis. 8. 127-135 (1998)
[Publications] Hiroaki Aikawa: "Norm estimate for the Green operator with applications" Proc.Conference in honor of Matis Essen. (to appear).
[Publications] Hiroaki Aikawa: "Integrability of superharmonic functions in a John domain" Proc.Amer.Math.Soc.(to appear).
[Publications] R.Fric and T.Nogura: "Rings of maps : Sequential convrgence and completion and strictness" Tatra Mt.Math.Publ.14. 137-143 (1998)
[Publications] A.V.Arhangel'skii, T.Nogura: "Relative sequentiality" Topology Appl.82. 49-58 (1998)
[Publications] V.Gutev and T.Nogura: "Selections for Vietoris-like hyperspace topologies" Proc.London Math.Soc.(to appear).
[Publications] S.Dolecki and T.Nogura: "Two-fold theorem on Frechetness of products" Czech.MAth.J.(to appear).
[Publications] V.Pestov and D.Shakmatov: "A relatively free topological group that is not varietal free" Colloq.Math.77. 1-8 (1998)
[Publications] Domitry Shakmatov: "A categorical version of the Lefschets-Nobeling-Pontryagin theorem on embedding compacta in R^n" Topology Appl.85. 345-349 (1998)
[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)

1998 Fiscal Year Annual Research Report

距離空間における位相次元の研究

Principal Investigator

服部 泰直 島根大学, 総合理工学部, 教授 (20144553)

Research Products

[Publications] Yasunao Hattori: "pi-embeddings and Dugundji extension theorems for generalized ordered spaces" Topology and its Applications. 84. 43-54 (1998)

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

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

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

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

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

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

[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)

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

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

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

[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).

[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).

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

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

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

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

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

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

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

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

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

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

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

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

[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)

服部泰直島根大学, 総合理工学部, 教授 (20144553)