Computability, corse topology and the dimensions of metric spaces
| Project/Area Number |
22540084
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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 | Shimane University |
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Principal Investigator |
HATTORI Yasunao 島根大学, 総合理工学研究科(研究院), 教授 (20144553)
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| Co-Investigator(Kenkyū-buntansha) |
KIMURA Makoto 島根大学, 総合理工学部, 教授 (30186332)
YAMAUCHI Takamitsu 島根大学, 大学院総合理工学研究科, 講師 (00403444)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUIKI Hideki 京都大学, 大学院人間環境学研究科, 教授 (10211377)
YOKOI Katsuya 東京慈恵会医科大学, 医学部, 教授 (90240184)
MATSUHASHI Eiichi 島根大学, 大学院総合理工学研究科, 講師 (60558518)
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| Research Collaborator |
CHATYRKO Vitalij Linkoping University (Sweden), Associate Professor
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 距離空間 / ドメイン / 次元 / 分離次元 / Martin位相 / Sorgenfrey位相 / 形式的球体 / 小帰納次元 / 位相次元 / 計算可能性 / Khalimsky 空間 / Alexandroff 空間 / Sorgenfrey型位相 / 半順序構造 / 粗いトポロジー / 位相空間 / 超空間位相 / 半順序集合 / Scott位相 / コンパクト化 / 集合値関数 / 選択関数 / 被覆次元 / 帰納的次元 |
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| Research Abstract |
The main topics of the project are the following: (1) The applications of topological method to the theory of the computability and domain theory; and (2) the dimensions of metric spaces and its applications. (1) An early study on the Martin topology on the domain of the formal balls of a metric space suggested an importance of the Sorgenfrey-type topologies on the real line. We investigated several Sorgenfrey-type topologies, and we have a condition that a such topology is homeomorphic to the Sorgenfrey topology. We also have a test subspace of the Khalimski space for determining the n-dimensionality of its subspaces. (2) We obtained Hurewicz formulas for large inductive dimensions on normal spaces with additional conditins. We also have a result on the transfinite separation dimension of a subspace of the Hilbert cube, and investigated an approach which unifies several small inductive dimensions of spaces including the Menger-Uryshon dimension ind and the separation dimension t.
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Report
(5 results)
Research Products
(50 results)
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[Presentation] Transfinite separation dimensions2012
Author(s)
Vitalij Chatyrko, Yasunao Hattori(発表者:服部泰直)
Organizer
International Conferece on Topology and the Related Fields
Place of Presentation
Nanjin Normal University, Nanjin, China
Year and Date
2012-09-23
Related Report
Invited
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