2012 Fiscal Year Final Research Report
Classification of Higher dimensional Erdos spaces by singular selectors
| Project/Area Number |
22540137
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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 | Ehime University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SHAKHMATOV Dmitri 愛媛大学, 理工学研究科, 教授 (90253294)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 順序数空間 / 連続弱選択関数 / 超空間 / 次元 |
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| Research Abstract |
It is well known that topologies generated by continuous weak selections are weaker than the original topologies. We call a space is CWS if the topology is generated by continuous weak selections. We have established the fundamental properties of CWS spaces and calculate the CWS numbers of several examples. Also we investigate the weak orderability of product spaces. As applications we show that if the product of a GO-space and a first countable space is weakly orderable, then the GO-space must be hereditarily paracompact. Also we have shown that a pseudocompact space without isolated point is homeomorphic to the Cantor set if and only ifits cube X×X×X is weakly orderable.
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Research Products
(16 results)
