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Is topologically simple simple? (1975)

Clark, W. E. ; Mukherjea, A. ; Tserpes, N. A.

Springer

Semigroup forum 11 (1975), S. 90-93

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ISSN: 1432-2137

Keywords: Primary 22A15 ; 20M10 ; 43AO5 ; Topological semigroup ; topologically ; simple ; completely simple semigroup ; left group ; invariant measures on topological groups

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02195256

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