An Observation on Initially $κ$-Compact Spaces

Çetin Vural

Published 2016-11-18Version 1

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 $\kappa .