| Project/Area Number |
10640095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kanagawa University |
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Principal Investigator |
YAJIMA Yukinobu Kanagawa University, Faculty of engineering, Professor, 工学部, 教授 (10142548)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| 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)
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| 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 |
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| Research Abstract |
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.
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