2013 Fiscal Year Final Research Report
Interplay between algebraic and topological closure operators, and existence of compact-like group topologies on abelian groups
| Project/Area Number |
22540089
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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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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 位相群 / トポロジー / コンパクト / 代数学 / 代数的閉包 |
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| Research Abstract |
We characterize potentially dense subsets of abelian groups G of size at most the power set of the continuum, and we show that the Markov-Zariski closure of a subset S of such a group G can be realized in some precompact group topology on G. (In particular, potential denseness of a set in G can be witnessed by some precompact group topology of G.) New metrizability criteria for compcat groups are obtained. We also provide various characterizations of Lie groups by means of controlling their zero-dimensional closed subgroups. Multiplier convergence theory of topological groups is developed.
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Research Products
(11 results)
