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Characterization of $$E\mathcal F$$-subcompactification. (English) Zbl 1164.22303
The focus of this paper is to study the universal $$E$$-subcompactification and the universal $$E\mathcal F$$-subcompactification. The authors continue the investigations of $$E$$-compactifications defined in an earlier paper by A. Fattahi, M. A. Pourabdollah and A. Sahleh [Int. J. Math. Math. Sci. 2003, No. 51, 3277-3280 (2003; Zbl 1028.22005)].
The authors define the notion of $$E\mathcal F$$-subcompactification of a semitopological semigroup $$S$$ as a compactification $$X$$ of $$S$$ such that its enveloping semigroup $$\Sigma _X$$ is a factor of $$S^{\mathcal F}$$.
They show that any compactification of $$S$$ has a universal $$E$$-subcompactification and that any $$m$$-admissible subalgebra $$\mathcal F$$ of the $$C^*$$-algebra $$C(S)$$ has a universal $$E\mathcal F$$-subcompactification.
Reviewer: Jan Paseka (Brno)
##### MSC:
 22A15 Structure of topological semigroups
##### Keywords:
semigroup; reductive semigroup
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