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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
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