2009 Fiscal Year Final Research Report
Study of the structure of the Markov-Zariski topology of a group and convergence properties of compact-like topological groups
| Project/Area Number |
19540092
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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 |
Geometry
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| Research Institution | Ehime University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NOGURA Tsugunori 愛媛大学, 理工学研究科, 教授 (00036419)
FUJITA Hiroshi 愛媛大学, 理工学研究科, 講師 (60238582)
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| Project Period (FY) |
2007 – 2009
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| Keywords | トポロジー / 代数学 / 位相群 / コンパクト / 収束性 |
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| Research Abstract |
We prove that Markov and Zariski topologies coincide for abelian groups, and we provide the description of the Markov-Zariski topology of an abelian group. Based on this description, we characterize counatable potentially dense susbets of abelian groups of size at most the continuum, as well as uncountable potentially dense subsets of torsion and divisible abelian groups. We also find a necessary and sufficient condition for the coincidence of Markov and Zariski topologies in the non-commutative case. The theory of group-valued function spaces is developed.
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