2012 Fiscal Year Final Research Report
New development in topology with the method of set theory
| Project/Area Number |
21740080
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
KADA Masaru 大阪府立大学, 理学系研究科, 准教授 (00312447)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 位相空間論 / 強制法 / 巨大基数公理 / 距離化可能空間 / コンパクト化 / リンデレーフ空間 / 無限ゲーム |
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| Research Abstract |
The subjects of this project include:
(1) Investigation into order structures consisting of sets of compatible metrics on metrizable spaces;
(2) Interplay between preservation of the Lindelof property under forcing extension and infinite games on Boolean algebras;
(3) The role of large cardinal axioms in bounding the cardinality of Lindelof spaces whose points are Gδ;
(4) Preservation of convergence of a sequence to a set under forcing extensions. Most of achievements in this project were obtained using not only traditional method in general topology but also set-theoretic method such as forcing.
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