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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

##### MSC:
 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D40 Remainders in general topology 54C20 Extension of maps
##### Keywords:
proximities; L-separation; compactification
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