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Primitive idempotents in convergence semigroups. (English) Zbl 0628.22001
R. J. Koch [Proc. Am. Math. Soc. 5, 828-833 (1954; Zbl 0056.027)] asked whether or not the set of primitive idempotents in a topological semigroup forms a closed set. The author presents an example of a convergence semigroup (not a topological semigroup) in which the primitive idempotents are not closed.
Reviewer: N.J.Rothman
MSC:
22A15 Structure of topological semigroups
22A20 Analysis on topological semigroups
22E99 Lie groups
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References:
[1] CHOW H. L.: Primitive idempotents in semigroups. Semigroup Forum, Vol. 10 (1975), 373-374. · Zbl 0308.22003
[2] KOCH R. J.: Remarks on primitive idempotents in compact semigroups with zero. Proc. Amer. Math. Soc. 5 (1954), 828-833. · Zbl 0056.02704
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