The considerations of M_3 problems from a new point of view
| Project/Area Number |
15540098
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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 Masami Kanagawa Univ., Faculty of Engineering, Prof., 工学部, 教授 (60215598)
KEMOTO Nobuyuki Oita Univ., Faculty of Education and Welfare Science, Prof., 教育福祉科学部, 教授 (70161825)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | M_3-space / normality / covering property / normal cover / product / infinite product / Σ-product / ordinal / M_3-空間 / M_1-空間 / 有限積空間 / 長方形の組分 / ベースパラコンパクト / 長方形 / パラコンパクト / rectangular |
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| Research Abstract |
The class of M_3-spaces seems to be one of the most important classes which contain metric spaces and CW-complexes. The problem of M_3-spaces which is deeply related to our results is that of the equivalence of normality and countable paracompactness of products with one M_3 factor.
This problem was submitted in 1992 and it is still open. However, we have recognized that it is necessary for it to study the covering properties of products with an M3 factor. In 2003, we began to study the new concept called base-paracompactness of such products. This concept was considered rather somewhat special. In 2004, this study was suddenly, developed as the general arguments of characterizations for normal covers of products. An essential idea in there is to use the concept of rectangular refinements for products. In 2005, we proved the same characterizations for normal covers of infinite products. Generally, finite products and infinite products are so different that their technique used there are also quite different. So it should be surprising to obtain the same results for both products. Moreover, using our techniques used here, we could give an affirmative answer to one of the problems concerning the normality of Σ-products, which was raised in 1989.
Nobuyuki Kemoto has been mainly studied the normality and some covering properties of the products of two subspaces of ordinals. They axe so special that it is possible to obtain many surprising results in this world. Masami Sakai has also obtained many results for function spaces and free topological groups, which will be related to the above results in the near future.
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Report
(4 results)
Research Products
(59 results)
