Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||Kanagawa University|
YAJIMA Yukinobu Kanagawa University, Faculty of engineering, Professor, 工学部, 教授 (10142548)
SAKAI Kazuhiro Kanagawa University, Faculty of engineering, Professor, 工学部, 助教授 (30205702)
SAKAI Masami Kanagawa University, Faculty of engineering, Professor, 工学部, 教授 (60215598)
|Project Period (FY)
1998 – 1999
Completed(Fiscal Year 1999)
|Budget Amount *help
¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥600,000 (Direct Cost : ¥600,000)
|Keywords||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 :
 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.
 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.
 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.
 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.
 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.
 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.