Subsets of \(C^*(X)\) generating compactifications (Q1109365)

From author's summary: ``The purpose of this paper is to characterize those subsets of \(C^*(X)\) which generate compactifications of X. A number of necessary and sufficient conditions for two subsets of \(C^*(X)\) to generate the same compactification are given. A certain assertion is shown to be equivalent to the continuum hypothesis. Another assertion is shown to be equivalent to the condition: \(n^{\aleph_ 0}=n\) whenever \(cf(n)>\aleph_ 0.''\)