Abstract
In this note we determine when topological simplicity of a subsemigroup implies its simplicity. A measure theoretic approach is used. The main result is: In a locally compact completely simple semigroup whose maximal subgroups are compact, every subsemigroup which is either locally compact or of non-empty interior is completely simple. As a corollary, we have: In a compact semigroup, any topologically simple subsemigroup which is either locally compact or of non-empty interior is simple.
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References
Berglund, J.F. and K.H. Hofmann,Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math: 42, Springer-Verlag, Berlin, Heidelberg and New York, 1967.
Chow, H.L.,In a compact semigroup, are topologically simple subsemigroups also simple?, Amer. Math. Monthly 82 (1975), 155–156.
Clifford, A.H. and G.B. Preston,The algebraic theory of semigroups, I,II. Math. Surveys no. 7, Amer. Math. Society, Providence, 1961,1967.
Mukherjea, A. and N.A. Tserpes,Idempotent measures on locally compact semigroups, Proc. Amer. Math. Soc. 29 (1971), 143–150.
Rothman, N.J. and M.W. Schuh,Laplace transforms on vanishing algebras, Semigroup Forum 8 (1974), 189–214.
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Communicated by Karl Heinrich Hofmann
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Clark, W.E., Mukherjea, A. & Tserpes, N.A. Is topologically simple simple?. Semigroup Forum 11, 90–93 (1975). https://doi.org/10.1007/BF02195256
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DOI: https://doi.org/10.1007/BF02195256