An Observation on Initially $\kappa$-Compact Spaces

Abstract

In \cite{Chaber}, Chaber has proved that countably compact spaces with a quasi $G_{\delta }$-diagonal are compact. We prove that initially $\kappa$% -compact spaces with a quasi $G_{\kappa }$-diagonal are compact, for any infinite cardinal $κ.

arXiv comment3 pages, corrected typos, made some revision in the exposition