| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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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