2012 Fiscal Year Final Research Report
A study on Scheepers' conjecture of special subsets of reals in view of a sequence of upper semi-continuous functions
| Project/Area Number |
22540154
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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 神奈川大学, 理学部, 教授 (60215598)
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| Co-Investigator(Renkei-kenkyūsha) |
YAJIMA Yukinobu 神奈川大学, 工学部, 教授 (10142548)
OHTA Haruto 静岡大学, 教育学部, 教授 (40126769)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 数学基礎論 |
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| Research Abstract |
Concerning Scheepers’ conjecture on special subsets of the real line and pseudo-normal convergence of continuous functions in a function space Cp(X) with the topology of pointwise convergence, we tried to answer the conjecture in view of a sequence of upper semi-continuous functions. We found that a Pixley-Roy hyperspace is useful to consider Scheepers’ conjecture. We obtained a characterization for a Pixley-Roy hyperspace is Frechet-Urysohn or has the discrete countable chain condition. Moreover, concerning selective separability which is connected with Scheepers’ conjecture, we gave answers to some open problems.
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