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Compactifications and L-separation. (English) Zbl 0675.54022
For a space X, let \(C^*(X)\) denote the algebra of all bounded real- valued continuous functions on X. Let \({\mathcal D}(X)\) denote the family of all subsets of \(C^*(X)\) which determine a compactification of X. The author proves that if \(F\in {\mathcal D}(X)\), \(G\subseteq C^*(X)\) and F is L-separated by G (in the sense of J. L. Blasco), then \(G\in {\mathcal D}(X)\) and the compactification determined by F is smaller than or equal to the compactification determined by G.
Reviewer: J.van Mill

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D40 Remainders in general topology
54C20 Extension of maps
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