Multicoherence and compactifications

Abstract

Let X be a connected, locally connected Tychonoff space. Let r(X) (respectively r(0)(X)) denote the multicoherence degree (respectively open multicoherence degree) of X. Let beta X be the Stone-Cech compactification of X and, if X is locally compact, let gamma X be the Freudenthal compactification of X. In this paper, we prove that if X is normal, then r(X) = r(beta X) and r(0)(X) = r(0)(beta X) and if X is locally compact, then r(gamma X) = min{r(Z): Z is a compactification of X}.