2013 Fiscal Year Final Research Report
A shape theoretical approach to fractal geometry
| Project/Area Number |
23540086
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kobe University |
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Principal Investigator |
MIYATA Takahisa 神戸大学, 人間発達環境学研究科, 教授 (30280390)
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| Project Period (FY) |
2011 – 2013
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| Keywords | shape theory / inverse system / metric space / normal sequence / asymptotic dimensiom / Assouad-Nagata dimension / フラクタル幾何学 |
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| Research Abstract |
Shape theory is known as a homotopy theory for topological spaces with locally bad behavior. Fractal, on the other hand, is one of the spaces carrying the notion of distance, and is known as a metric space with locally complicated structures. In this project, we apply the theory of shape, in particular, its categorical aspects, to find the properties of fractals, or even general metric spaces. In particular, we have shown that the notion of inverse system, which is one of the most important approaches to shape theory, and the notion of normal sequence, which is one of the most important notions in the theory of topological spaces, have strong connections to metric spaces.
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