| 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
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| Project Period (FY) |
1998 – 2000
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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 |
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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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