2009 Fiscal Year Final Research Report
A study on special subsets of real numbers derived from local properties of function spaces and their critical cardinalities
| Project/Area Number |
19540151
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kanagawa University |
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Principal Investigator |
SAKAI Masami Kanagawa University, 工学部, 教授 (60215598)
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| Co-Investigator(Kenkyū-buntansha) |
YAJIMA Yukinobu 神奈川大学, 工学部, 教授 (10142548)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 数学基礎論 |
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| Research Abstract |
For a topological space X, we denote by Cp(X) the space of all continuous functions with the topology of pointwise convergence. It is known that a local property of Cp(X) can be characterized in terms of a covering property of X. For example, Gerlits and Nagy showed that Cp(X) is Frechet if and only if X is a γ-set. A γ-set is strong measure zero, so some local properties of Cp(X) are related with some singular sets of reals appeared in descriptive set-theory. We studied some relations between local properties of Cp(X) and singular sets X of reals, and answered some open problems posed by Scheepers, Bukovsky and so on.
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