Research on computable structures of continuous spaces like the real number through representation in bottomed sequences
| Project/Area Number |
18500013
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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 |
Fundamental theory of informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
TSUIKI Hideki Kyoto University, 人間・環境学研究科, 准教授 (10211377)
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| Research Collaborator |
服部 泰直 島根大学, 総合理工学部, 教授
大田 春外 静岡大学, 教育学部, 教授
山田 修司 京都産業大学, 理学部, 教授
八杉 真理子 京都産業大学, 名誉教授
辻井 芳樹 京都産業大学, 理学部, 教授
森 隆一 京都産業大学, 理学部, 教授
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 実数計算 / グレイコード / ドメイン理論 / 位相空間論 / 不定元 / 双曲位相 / Lawson位相 / independent subbase / 計算可能性解析学 / グレイコ-ド / 独立部分基 / 有限時間計算可能性 / 距離空間 / ボトム入り文字列表現 / 解析学における計算可能性 / 実数 / 位相構造 / 計算構造 |
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| Research Abstract |
The computational structure of the reals and other topological spaces are studied mainly with the method of embedding a space into the set of infinite sequences with bottoms. Some computationally natural properties of an embedding, such as the recursiveness of the definition and the non-redundancy of each digit in a code sequence, are investigated through their characterization in general topological terms, and some characterizations of spaces with such an embedding are given. Other topics such as constant time computability preserving conversions, and the relation between the Lawson topology of the space of formal balls and the hyperbolic topology of a metric space, are also investigated.
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Report
(6 results)
Research Products
(35 results)
