2016 Fiscal Year Final Research Report
Topology of non-separable infinite-dimensional manifolds, function spaces and hyperspaces
| Project/Area Number |
15K17530
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kanagawa University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2017-03-31
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| Keywords | 無限次元多様体 / LF-多様体 / 写像空間 / 冪空間 |
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| Outline of Final Research Achievements |
The aim of this research is to develop the theory of non-separable infinite-dimensional manifolds by investigating topological properties of non-separable LF-manifolds and topological structures of function spaces and hyperspaces. In this research, I gave necessary and sufficient conditions on a space whose hyperspace of compact subset is homeomorphic to a non-separable Hilbert space, and on a space whose hyperspace of finite subsets is homeomorphic to the linear subspace spanned by the canonical orthonormal basis of a non-separable Hilbert space. I could not achieved good results in the study on the fundamental theorems of LF-manifolds, and in the study on detecting infinite-dimensional manifolds among function spaces, but obtained new knowledge for future research.
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| Free Research Field |
位相幾何学
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