2010 Fiscal Year Final Research Report
A study of extension problems of partitions of unity on topological spaces
| Project/Area Number |
19740027
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Takasaki City University of Economics |
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Principal Investigator |
YAMAZAKI Kaori Takasaki City University of Economics, 経済学部, 准教授 (80301076)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 位相幾何 / 1の分割 / 連続関数の拡張 / 線形拡張子 / 拡張作用素 / バナッハ束 / 挿入定理 |
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| Research Abstract |
On extension problems of partitions of unity, we study various extenders on topological spaces. In particular, we give a condition which characterizes a normed space to be reflexive by using linear closed convex extenders. This provides a negative answer to a question asked by Heath and Lutzer in 1974. Moreover, we give a theorem which shows variations between linear closed convex extenders and monotone extenders.
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