2022 Fiscal Year Final Research Report
| Project/Area Number |
20K03721
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 12030:Basic mathematics-related
|
|---|
| Research Institution | Kagoshima University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
吉田 聡 公立鳥取環境大学, 人間形成教育センター, 教授 (00455437)
|
|---|
| Project Period (FY) |
2020-04-01 – 2023-03-31
|
| Keywords | 関係 / 位相 / 各点連続 / 点列連続 / 構成的数学 |
|---|
| Outline of Final Research Achievements |
The following results on continuity of relations are obtained in classical mathematics. (1) 2 equivalent conditions to the continuity which studied in Weihrauch's computable analysis; (2) a generalization of Berge’s upper semicontinuity, 5 conditions which are equivalent to it, and a sufficient condition for it to be equivalent to sequential continuity
Also, in constructive analysis, the following results are obtained. (3) a fact that 5 classically equivalent conditions are divided into 2 groups: conditions equivalent to pointwise continuity and to sequential continuity, and a sufficient condition for all 5 conditions are equivalent
|
| Free Research Field |
数学基礎関連
|
| Academic Significance and Societal Importance of the Research Achievements |
関係は非決定的な振る舞いを数学的に取り扱うための最も基本的な道具である．関係の連続性の概念は分野ごとの利用目的に応じていくつも提案されてきているが，これらに関する一般の位相空間論的観点からの系統的な研究はほとんどなされてこなかった．本研究では関係の連続性の統一的で系統的な理解の初期段階を与えた．つまり，本研究の成果は位相空間の間の非決定性理論の基盤構築と位置づけられ，連続関係の概念を基礎とする数学の展開に繋がることが期待される．
|
