2013 Fiscal Year Annual Research Report
可換群における代数的閉包と群位相での閉包の相互作用及びコンパクト型群位相化の研究
| Project/Area Number |
22540089
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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 | トポロジー / 代数学 / 位相群 / コンパクト / 代数的閉包 |
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| Research Abstract |
We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The ``compact-like'' properties we consider include (local) compactness, (local) omega-boundedness, (local) countable compactness, (local) precompactness, (local) minimality and sequential completeness. Below is a sample of our characterizations:
(i) A topological group is a Lie group if and only if it is locally compact and has no infinite compact metric zero-dimensional subgroups.
(ii) An abelian topological group group G is a Lie group if and only if G is locally minimal, locally precompact and all closed metric zero-dimensional subgroups of G are discrete.
(iii) An abelian topological group is a compact Lie group if and only if it is minimal and has no infinite closed metric zero-dimensional subgroups.
(iv) An infinite topological group is a compact Lie group if and only if it is sequentially complete, precompact, locally minimal, contains a non-empty open connected subset and all its compact metric zero-dimensional subgroups are finite.
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| Current Status of Research Progress |
Reason
25年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
25年度が最終年度であるため、記入しない。
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Research Products
(4 results)
