Asymptotic dimension, topological dimension on metric spaces and topological structures of computational models
| Project/Area Number |
26400089
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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, 学内共同利用施設等, 学長 (20144553)
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| Co-Investigator(Kenkyū-buntansha) |
渡邉 忠之 島根大学, 学術研究院理工学系, 講師 (70467447)
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| Project Period (FY) |
2014-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ドメイン / 位相 / 次元 / 計算可能性 / 順序構造 / 距離空間 / 位相空間 / 次元論 / 形式的球体 / Sorgenfrey位相 / continuous bijection / reversible space / Alexandroff space / アレクサンドロフ空間 / Khalimski空間 / Khalimski直線 / リバーシブル空間 / 位相幾何学 / 計算モデル |
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| Outline of Final Research Achievements |
D. Scott gave a mathematical foundation for denotational semantics by pointed that continuous lattices could be used to analyze the semantics of the program written by high-level programming languages. Then continuous lattices are studying by the motivations from both of the theory of computation and mathematics (algebra, topology and analysis, etc.)
In the research project, we study domain theory by topological approach, topological properties motivated by the study of domain theory and dimension theory of several topological spaces. Especially, we study special types of topologies on the space of the real numbers motivated by the study of the Martin topology of the domain of the formal balls of the real numbers, and several topological properties of n-dimensional Khalimsky space.
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| Academic Significance and Societal Importance of the Research Achievements |
ドメイン理論は計算機科学に数学的観点から理論的基盤を与える重要な研究領域である。ドメイン理論は、代数学、トポロジー、解析学等多様なアプローチが可能な領域であり、計算機科学への応用のみでなく純粋理論としても学術的意義は高い。本研究では主にドメインの位相数学的アプローチによる研究を進め、ドメインの順序構造を位相を用いて解析し、さらに、位相数学の課題として次元論と関連も含めて研究を推進したことは、計算機科学への応用と位相数学の発展の両面で意義深い。
また、10か国以上の海外協力研究者との連携によるドメイン理論とトポロジー両分野の国際的ネットワークが構築されるなど、国際連携が推進された。
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Report
(7 results)
Research Products
(52 results)
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[Presentation] Hereditarily reversible spaces2016
Author(s)
Yasunao Hattori
Organizer
2016 International Conference of the Honam Mathematical Society
Place of Presentation
Chonbuk National University, Jeonju, South Korea
Year and Date
2016-06-16
Related Report
Int'l Joint Research / Invited
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