Structure of compact-like abelian groups and realization of Markov density by a group topology

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400091
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Ehime University
• Principal Investigator: SHAKHMATOV Dmitri 愛媛大学, 理工学研究科(理学系), 教授 (90253294)
• Project Period (FY): 2014-04-01 – 2018-03-31
• 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.

Free Research Field

位相群論