2015 Fiscal Year Final Research Report
Investigation of topological properties of hyperspaces from the theory of products: seeking set theoretical approaches
| Project/Area Number |
23540149
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 | Oita University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | topology / products / hyperspaces / ordinal numbers / ordered spaces / elementary submodels |
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| Outline of Final Research Achievements |
Original purposes of this research were, using some set theoretical techniques,to investigate topological properties of hyper spaces by means of product theory. As results, applying set theoretical tool so called the elementary submodels, we have some results about normality or other topological properties of hyperspaces of all closed sets or all compact sets. On the other hand, whether the hyperspace of all subsets of the natural numbers is countably metacompact remains open. But we obtain an answer to the problem whether the products of two generalized ordered are countably metacompact, which has remained open for twenty years.
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| Free Research Field |
数物系科学
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