A construction involving inverse limits
Recall that a topological space is called an \(F\)-space if any two disjoint open \(F_\sigma\) subsets have disjoint closures; and that a continuous mapping \(f:X\to Y\) is called irreducible if \(f[X] = Y\) and \(f[F] = Y\) implies \(F = X\) for every closed set \(F\subset X\). The main result (Theorem 4.3) states that for any compact space \(X\) there exists a compact \(F\)-space \(FX\) and an irreducible mapping \(f:FX\to X\) such that the weight of \(FX\) is minimal possible, that is, \(w(FX) = w(X)^\omega\). The space \(FX\) above is constructed using inverse limits. The result is very clearly motivated and put into the right context of related results.
scientific article; zbMATH DE number 7401480