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 |
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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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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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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 / topological group / pseudocompact / selective property / variety of groups / reflexive group / SSGP group / divisible rank / MinAP group / sequentially compact / omega-bounded group / weakly pseudocompact / completeness properties / direct products / direct sums / topological vector space / dual group / multiplier convergence / compact / connected space / Markov problem / unconditionally closed / abelian group / group topology / precompact group / minimal group |
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| 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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Report
(5 results)
Research Products
(40 results)
