Abstract
Let X be a completely regular Hausdorff space and let H be a subset of C ∗( X) which separates points and closed sets. By embedding X into a cube whose factors are indexed by H, a Hausdorff compactification e H X of X is obtained. Given two subsets F and G of C ∗( X) which separate points from closed sets, in the present paper we obtain a necessary and sufficient condition for the equivalence of e F X and e G X. The condition is expressed in terms of the space X and the sets F and G alone, herewith solving a question raised by Chandler.
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