| Project/Area Number |
14540059
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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 University of Tsukuba, Garduate School of Pure and Applied Sciences, Associate Professor, 大学院・数理物質科学研究科, 助教授 (50036084)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMURA Kazuhiro University of Tsukuba, Garduate School of Pure and Applied Sciences, Associate Professor, 大学院・数理物質科学研究科, 助教授 (40204771)
YAMAZAKI Kaori University of Tsukuba, Garduate School of Pure and Applied Sciences, Instructor, 大学院・数理物質科学研究科, 助手 (80301076)
YAGASAKI Tasuhiko Kyoto Institute of Technology, Department of Mathematics, Associate Professor, 工芸学部, 助教授 (40191077)
IWAMOTO Yutaka Yuge National College of Maritime Technology, Associate Professor, 助教授 (10300641)
UEHARA Shigenori Takamatsu National College of Technology, Assistant Professor, 講師 (80321496)
加藤 久男 筑波大学, 数学系, 教授 (70152733)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | infinite-dimensional manifold / universal space / topology / hyperspace / mapping space / AR, ANR / absolute Borel class / Nobeling space / 下半連続実数値関数 / Hillert立方体 / 有限部分集合 / 非可分 / Nobeling空間 / Hausdorff距離位相 / Fell位相 / 閉凸集合 / Hilbert立方体 / Hilbert空間 / Hyperspace / closed convex set / normed linear space / Hausdorff metric / Attouch-Wets topology / Wijsman topology / uniform AR / AR |
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| Research Abstract |
Throughout three years, making our efforts to achieve the following three intensions in this subject, we have many results relating to each item.
1.Characterizing universal spaces for various classes of non-separable spaces which had not been investigated ;
2.In order to enrich the theory of infinite-dimensional manifolds, finding natural examples of non-separable infinite-dimensional manifolds and investigating their topological and geometrical structures ;
3.Studying other subjects related to this subject and applying each others.
For the first item, by the joint work of Sakai and his student Yaguchi and the work of the other student Mine, Bestvina-Mogilski's theory of absorbing sets have been extended to non-separable absolute Borel classes. By Iwamoto's studies, it have been clear that Ageev's proof of the characterization of Nobeling spaces contains gaps. The complete proof is excepted.
For the second item, we have many results concering hyperspaces and mapping spaces. The hyperspace of non-empty closed sets in a non-compact metric space is studied by introducing various topologies instead of the classical Vietoris topology, that is, the Hausdorff metric topology, the Fell topology, the Attouch-Wets topology, the Wijsman topology, etc. Sakai has studied with Banakh, Yang, Kubis and his students, Kurihara, Yaguchi and Mine, and obtained results that such hyperspaces are homeomorphic to infinite-dimensional universal spaces for some classes and that they are AR's even if they are not known about the above. On the other hand, Yagasaki have been working on the spaces of embeddings and homeomorphisms and he have many results. Moreover, Uehara had a result concerning the spaces of upper semi-ccontinuous set-valued functions.
Concering the third item, there are results by Sakai and Sakai-Iwamoto and Kawamura and Yamazaki have many interesting results.
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