| Project/Area Number |
17K05251
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Shimane University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2017-04-01 – 2024-03-31
|
| Project Status |
Completed (Fiscal Year 2023)
|
| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | Whitney preserving map / graph-like continuum / inverse limit / decomposable continuum / indecomposable continuum / Whitneyの逆性質 / 射影極限 / D**-continuum / aposyndetic / Wilder-continuum / semiaposyndetic / Janiszewski continuum / D-continuum / Inverse limit / Chogoshvili-Pontrjagin予想 / superdendrite / Eulerian path / 複雑な連続写像 / 無限次元 / ペアノ連続体 |
|---|
| Outline of Final Research Achievements |
We proved the equivalence between weakly Whitney preserving maps, which map continua to graph-like continua, and arc-wise increasing maps, serving as a generalization of Eulerian paths. Additionally, We demonstrated that among surjective continuous mappings from closed intervals to n-dimensional cubes (space-filling curves), almost all such mappings are weakly Whitney preserving maps in a topological sense. Moreover, We strengthened a well-known counterexample to the Chogoshvili-Pontrjagin claim. Furthermore, We conducted research on inverse limits with uppee semi-continuous set-valued functions, deriving sufficient conditions for inverse limits to become indecomposable continua.
|
| Academic Significance and Societal Importance of the Research Achievements |
連続体間の特殊な連続写像であるweakly Whitney preserving mapがgraph-like連続体におけるEulerlian pathと等価であることを証明したことは、トポロジーとグラフ理論の境界領域の開拓への寄与であるといえる。また、昨今の射影極限の理論において、上半連続な集合値関数を結合関数とする射影極限が分解不可能になるための十分条件は、そのほとんどの場合が因子空間が閉区間の場合において与えられているが、本研究では因子空間を一般の連続体としており、本分野において大きな前進となっている。
|
