Research on "Classification of filters and subsets of reals with respect to selector, and convergence properties of hyperspacea"
| Project/Area Number |
15540125
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
NOGURA Tsugunori Ehime University, Faculty of Science, Professor, 理学部, 教授 (00036419)
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| Co-Investigator(Kenkyū-buntansha) |
SHAKHMATOV Dmitri Ehime University, Faculty of Science, Professor, 理学部, 教授 (90253294)
HIRAIDE Koichi Ehime University, Faculty of Science, Associate Professor, 理学部, 助教授 (50181136)
FUJITA Hiroshi Ehime University, Faculty of Science, Lecture, 理学部, 講師 (60238582)
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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 |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Selector / Hyperspace / Fell topology / Dimension / Vietoris topology / Countably compact / 連続選択関数 / Ginsburg's question / 積空間 / 可算コンパクト性 / 擬コンパクト性 / Ginsburg's problem |
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| Research Abstract |
We investigate topological properties of spaces which admit continuous (weak)selction and also the relationship between topological properties of hyperspaces and that of base spaces, especially convergence properties. The main results obtained by our project are as follows ;
(1)If X is homogeneous space, then countable (pseudo) compactness of hyperspace implies that of countable product of X. This gives a partial solution of Ginsburgs problem.
(2)We establishe that topologically welorderability of base space is equivalent to the existence of Fell continuous selection.
(3)There exists a space which admit a continuous weal selection but small inductive dimension can be taken any natural number.
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Report
(4 results)
Research Products
(18 results)
