Research of topological properties of metric spaces and dimensions

度量空间和维数的拓扑性质研究

• 批准号: 14540066
• 负责人: TANAKA Yoshio
• 金额: $ 1.98万
• 依托单位: Tokyo Gakugei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540066/
• 关键词: quotient spaces; k-spaces; k-networks; weak topologies; metric dimensions; compactifications; Riemannian manifolds; tangent sphere bundles; k-ネットワーク; コンパクト空間; 次元; 連続公理; 距離空間; 点列空間; quotient spaces; k-spaces; k-networks; weak topologies; metric dimensions; compactifications; Riemannian manifolds; tangent sphere bundles; k-ネットワーク; コンパクト空間; 次元; 連続公理; 距離空間; 点列空間

This research project is the investigations of topological properties around metric spaces, and dimensions related to metric spaces. The main objects of the research are the following :(A)Topological properties or structures of quotient spaces of metric spaces, and their product spaces(B)Metric spaces and dimensions(C)Compactifications in metric spaces, and their dimensions(D)Tangent sphere bundles, hyper surfaces in Riemannian manifold, and their dimensionsThe research on (A);(B);(C); and (D) has been done by Y.Tanaka mainly ; T.Goto ; T.Kimura and K.Morishita ; and M.Sekizawa, respectivelyConcerning (A), Y.Tanaka considered the following classic questions (1) & (2), and a question (3)(1)Characterize some topological spaces by means of certain nice quotient spaces of metric spaces(2)For k-spaces X, Y, what is a necessary and sufficient conditions for the product space X x Y to be a k-space?(3)For a space X having a certain k-network, or having a weak topology with respect to certain covering, investigate nice topological structures of the space XFor the above questions, Y.Tanaka obtained some nice answers or results in his (joint) papers in famous international journals, Topology and its Applications, Houston J.Math., or Topology Proceedings, and so on.Concerning (B)-(D), some nice results also obtained by the investigators in their (joint) papers in Topology and its Appl., Fund Math., or other international journals, etcThe details for these, containing related papers and science reports, etc., are given in our Research-Report (under this grant-in-aid for scientific research (14540066)), 2005. March (pp.1-340).

该研究项目是对度量空间周围拓扑特性的研究，以及与度量空间有关的尺寸。该研究的主要对象是：（a）度量空间的商及其产品空间的拓扑特性或结构（b）度量空间和尺寸（c）压缩度（c）压缩及其尺寸（d）切线球形的尺寸（d）切线，riemannian歧管中的超表面，以及他们的二元研究（b）； （D）主要由Y.Tanaka完成； T.Goto; T.Kimura和K.Morishita； and M.Sekizawa, respectivelyConcerning (A), Y.Tanaka considered the following classic questions (1) & (2), and a question (3)(1)Characterize some topological spaces by means of certain nice quotient spaces of metric spaces(2)For k-spaces X, Y, what is a necessary and sufficient conditions for the product space X x Y to be a k-space?(3)For a space X having a certain k-network, or having a weak关于某些覆盖的拓扑，调查上述问题的良好拓扑结构，Y.Tanaka在著名的国际期刊，拓扑，拓扑及其应用，休斯顿J.Math。或拓扑程序或拓扑程序中获得了一些不错的答案或结果。期刊等，其中包含相关论文和科学报告等的详细信息，请在我们的研究报告中（根据科学研究的这项拨款（14540066）），2005年。3月（第1-340页）。