NORMALITY AND COVERING PROFERITIES OF TOPOLOGICAL PROCUCT SPACES

拓扑产品空间的正规性和覆盖特性

• 批准号: 10640095
• 负责人: YAJIMA Yukinobu
• 金额: $ 0.7万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640095/
• 关键词: topological product; normality; covering property; regular net; metrization theorem; k-network; function space; shadowing property; LF-netted空間; 順序数; メタコンパクト; サブパラコンパクト; Special refinement

This study is mainly classified by the following six parts :[1] Characterizations of covering properties in terms of products :We prove some characterizations of metacompactness and submetacompactness in terms of products, and give a complete solution of a problem raised in 1992.[2] Covering properties of products of ordinals :We prove that most covering properties are equivalent in the products of ordinals, and that only subparacompactness is unexpectedly an exception there.[3] Normality of products with a generalized metric factor :Making use of regular nets, we introduced a new concept of generalized metric spaces, and prove the equivalence of normality and countable paracompactness in products with such a generalized metric factor.[4] Metrization theorems in terms of regular k-networks :We prove a natural metrization theorem in terms of regular k-networks. This gives a solution of a problem raised by Nagata.[5] Problems for k-networks and function spaces :M.Sakai has respectively answered two problems for k-networks raised by Lin and Tanaka, and he has also solved a problem for function spaces raised by Bella.[6] Shadowing properties on compact metric spaces :K.Sakai have given a partial answer to the problem of whether shadowing property and Lipschitz shadowing property are equivalent on compact metric spaces.

本研究主要分为以下六个部分：[1]乘积覆盖特性的表征：我们证明了乘积方面的超紧性和亚紧致性的一些表征，并对1992年提出的一个问题给出了完整的解决方案。[2]序数乘积的覆盖性质：我们证明大多数覆盖性质在序数乘积中是等价的，并且只有次仿紧性是意外的例外。[3]具有广义度量因子的乘积的正态性：利用正则网络，引​​入了广义度量空间的新概念，并证明了具有广义度量因子的乘积的正态性和可数拟紧性的等价性。 [4]正则 k 网络方面的度量化定理：我们证明了正则 k 网络方面的自然度量化定理。这给出了 Nagata 提出的问题的解决方案。[5] k网络和函数空间问题：M.Sakai分别回答了Lin和Tanaka提出的两个k网络问题，并且还解决了Bella提出的一个函数空间问题。[6]紧度量空间上的阴影性质：K.Sakai对于紧度量空间上的阴影性质和Lipschitz阴影性质是否等价的问题给出了部分答案。

项目成果

矢島幸信: "Special refinements and their applications on products"Topology and its Applications.

Yukinobu Yajima：“特殊改进及其在产品上的应用”拓扑及其应用。

Kazuhiro Sakai: "The OE-property of diffeomorphisms"Discrete and Continuous Dynamical Systems. 4. 581-591 (1998)

Kazuhiro Sakai：“微分同胚的 OE 性质”离散和连续动力系统。

矢島幸信: "Special refinements and their applications on products"Topology and its Applications..

Yukinobu Yajima：“特殊改进及其在产品上的应用”拓扑及其应用..

酒井政美、玉野研一、矢島幸信: "Regular networks for metrizable spaces and Lavnev spaces" Bulletin of the Polish Academy of Sciences. 46. 121-133 (1998)

Masami Sakai、Kenichi Tamano、Yukinobu Yajima：“可度量空间和拉夫涅夫空间的正则网络”波兰科学院通报 46. 121-133 (1998)。

矢島幸信: "Analogous results to two classical characterizations of covering properties by products"Topology and its Applications. 84. 3-7 (1998)

Yukinobu Yajima：“乘积覆盖属性的两个经典表征的类似结果”拓扑及其应用 84. 3-7 (1998)。