2009 Fiscal Year Final Research Report
On the structure of computability on metric spaces, dimension and the complexities of descriptive set theory
| Project/Area Number |
19540086
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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 | Shimane University |
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Principal Investigator |
HATTORI Yasunao Shimane University, 総合理工学部, 教授 (20144553)
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| Co-Investigator(Kenkyū-buntansha) |
TSUIKI Hideki 京都大学, 大学院・人間・環境学研究科, 准教授 (10211377)
YOKOI Katsuya 東京慈恵会医科大学, 医学部, 教授 (90240184)
MAEDA Sadahiro 佐賀大学, 理工学部, 教授 (40181581)
KIMURA Makoto 島根大学, 総合理工学部, 教授 (30186332)
NOGURA Tsugunori 愛媛大学, 大学院・理工学研究科, 教授 (00036419)
FURUMOCHI Tetsuo 島根大学, 総合理工学部, 教授 (40039128)
YAMAUCHI Takamitsu 島根大学, 総合理工学部, 講師 (00403444)
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| Project Period (FY) |
2007 – 2009
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| Keywords | トポロジー / 情報基礎 / 距離空間 / ドメイン / 次元 |
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| Research Abstract |
We studied about the computability of metric spaces from the topological point of view. We also studied on set-theoretic topology and dimension theory of topological spaces. In particular, we studied the relations between the order and topological structures on the domains of the formal balls of metric spaces. Concerning dimension theory, we investigated the inductive dimension modulo absolute multiplicative class M(α) and additive class A(α), and constructed the examples which show the differences of the values of these dimensions. We also improved the additive theorem and the product theorem for the inductive dimensions. We also considered the spaces which are finite union of locally compact subspaces and gave a characterization of strong paracompactness by means of the selection of multi-valued mappings
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