| Project/Area Number |
10640060
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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 | University of Tsukuba |
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Principal Investigator |
SAKAI Katsuro Inst. of Math., Univ. of Tsukuba, Assoc. Prof., 数学系, 助教授 (50036084)
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| Co-Investigator(Kenkyū-buntansha) |
IWAMOTO Yutaka Yuge National College of Maritime Tech., Lect., 講師 (10300641)
YAGASAKI Tatsuhiko Dept. of Mech. Syst. Engin., Kyoto Instit. Tech., Assoc. Prof., 工芸学部, 助教授 (40191077)
KAWAMURA Kazuhiro Inst. of Math., Univ. of Tsukuba, Assoc. Prof., 数学系, 助教授 (40204771)
UEHARA Shigenori Takamatsu National College of Tech., Lect., 講師 (80321496)
AKAIKE Yuji Kure National College of Tech., Lect., 講師
加藤 久男 筑波大学, 数学系, 教授 (70152733)
山崎 薫里 筑波大学, 数学系, 助手 (80301076)
保科 隆雄 筑波大学, 数学系, 教授 (00015893)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | infinite-dimenisonal manifold / absolute neighborhood retract (ANR) / space of mappings / hyperspace / Menger manifold / universal space / proper n-shape theory / strong n-shape theory / Attouch-Wets位相 / Fell位相 / Hilbert空間 / Hilbert cube / strong universal / discrete approximation property / 無限次元多様体 / ANR / homotopy deuse / homotopy type / homeomorpliesm group / Menger多様体 / proper homotopy / strong n-shape / 上半連続集合値関数 / pseudo-interior / Banach-Mazur compactum / 帰納的極限 / proper n-shape |
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| Research Abstract |
1. Infinite-Dimensional Manifolds and ANR Theory.
In this part, we have many results in the following researches :
(1) Characterizations of bitopological infinite-dimensional manifolds (Sakai-Banakh) ;
(2) Studies on free topological semilattices (Sakai-Banakh) ;
(3) Direct limits of Banach-Mazur compacta (Sakai-Kawamura-Banakh) ;
(4) Studies on spaces of homeomorphisms and embeddings (Yagasaki) ;
(5) Spaces of Peano and ANR continua (Yagasaki) ;
(6) Characterizations of ANR's (Sakai).
Recently, we have made some progress in the following two studies, whose development are expected :
(7) Maps from mapping spaces to a hyperspaces (Yagasaki) ;
(8) Hyperspaces of closed sets of non-compact metric spaces (Sakai-Kurihara-Yang).
2. Menger Manifolds and n-Shape Theory.
In this part, we have many results in the following researches :
(1) Dynamics on Menger manifolds (Kato-Kawamura-Tuncali-Tymchatyn) ;
(2) Dimension of the homeomorphism group of Menger compacta (Kawamura-Brechner) ;
(3) Lusternik-Schnirelmann type invariants concerning Menger manifolds (Kawamura) ;
(4) Groupe actions on Menger curve (Kawamura) ;
(5) An application to a universal space for a class of closed images of metric spaces (Kawamura-Tuda) ;
(6) Studies on proper n-shape theory (Sakai-Akaike) ;
(7) Formulation of strong n-shape (Sakai-Iwamoto).
3. In relation to this project, we invited Prof. Ageev (Belorussia) to learn about his research on the characterization of Nobeling spaces. Now, we are ready to work together with him, and further joint studies with him are expected.
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