| Project/Area Number |
17K05352
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kanagawa University |
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Principal Investigator |
SAKAI MASAMI 神奈川大学, 理学部, 教授 (60215598)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 関数空間 / Scheepers予想 / Menger / Menger property / projectively Menger / 数学基礎論 / 幾何学 |
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| Outline of Final Research Achievements |
The purpose of this study was to solve Scheepers' conjecture on the relation between a topological property of X and a local property of the function space Cp(X) with the topology of pointwise convergence. Concerning Scheepers' conjecture, we obtained the following results. (1) we gave a characterization of X for Cp(X) to be projective Menger, and gave some implications of topological properties appeared in Scheepers' conjecture, (2) we showed that under some weak local property of X and Y, if Cp(X) and Cp(Y) are linearly homeomorphic and X is Menger, the Y is also Menger, where this is a partial answer to Arhangelskii's problem.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究期間ではScheepers予想の最終解決には至らなかったが、周辺の問題の解決に向けてはいくつかの進捗が得られ、今後の研究の進展に寄与すると思われる。特に、研究成果の概要で述べられた(2)の結果は、実数の部分集合の間ではMenger性は関数空間の間の線形同相で保存されることを示し、今後の研究方向を定めるうえで重要と思われる。
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