2017 Fiscal Year Final Research Report
Structure of compact-like abelian groups and realization of Markov density by a group topology
Project/Area Number |
26400091
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Ehime University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Keywords | 位相群 / トポロジー / 代数学 / コンパクト / 連結性 / 小部分群 / 疑コンパクト |
Outline of Final Research Achievements |
We confirm 70 years old conjecture of Markov concerning the algebraic structure of connected groups in the class of abelian groups. Answering a question of Comfort and Gould, we completely describe the algebraic structure of abelian topological groups having the small subgroup generating property. We construct a countable free closed non-relexive subgroup in the product of continuum many integers. We introduce a notion of selectively sequentially pseudocompact space and study basic properties of this new subclass of pseudocompact spaces. Answering a question of Tkachenko, we prove that a weakly pseudocompact precompact group is pseudocompact.
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Free Research Field |
位相群論
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