Weight of a compactification and generating sets of functions (Q1110846)

In the first part, some consequences of Stone-Weierstrass theorem to generating compactifications are shown (e.g. if F, \(G\subset C^*(X)\), \(\bar F=\bar G\) in the sup-norm topology then F, G generate the same compactification). Then it is proved that if bX is a compactification of X, \(w(bX)>w(X)\), then \(w(bX)=\omega \cdot \min \{| F|:\) \(F\subset C^*(X)\), F determines bX\(\}\). The last part studies the lattice of the compactifications bX of X with \(w(bX)=w(X)\).