Multicoherence and compactifications

Let X be a connected, locally connected Tychonoff space. Let r(X) (respectively r0(X)) denote the multicoherence degree (respectively open multicoherence degree) of X. Let βX be the Stone Čech compactification of X and, if X is locally compact, let γX be the Freudenthal compactifica tion of X. In this paper, we prove that if X is normal, then r(X) = r(βX) and r0(X) = r0(βX) and if X is locally compact, then r(γX) = min{r(Z): Z is a compactification ofX}.