On Wallman-type compactifications (Q5916369)

The main result is the following: Let \(X\) be a Tychonoff space, \(bX\) be a compactification of \(X\) and \(ZX\) be a Wallman-type compactification of \(X\) satisfying \(bX\leq ZX\). Then there exists a Wallman-type compactification \(Z'X\) such that \(bX\leq Z'X\leq ZX\), \(w(Z'X)\leq w(bX)\), \(\dim Z'X\leq\dim ZX\).