Communications of the
Korean Mathematical Society CKMS

In this paper, we show that if the minimal basically disconnected cover $\Lambda X_i$ of $X_i$ is given by the space of fixed $\sigma Z(X)^\#$-ultrafilters on $X_i$ $(i = 1, 2)$ and $\Lambda X_1$ $\times$ $\Lambda X_2$ is a basically disconnected space, then $\Lambda X_1$ $\times$ $\Lambda X_2$ is the minimal basically disconnected cover of $X_1\times X_2$. Moreover, observing that the product space of a $P$-space and a countably locally weakly Lindel\" of basically disconnected space is basically disconnected, we show that if $X$ is a weakly Lindel\" of almost $P$-space and $Y$ is a countably locally weakly Lindel\" of space, then $(\Lambda X$ $\times$ $\Lambda Y$, $\Lambda_X \times \Lambda_Y$) is the minimal basically disconnected cover of $X \times Y$.

Keywords: basically disconnected space, covering maps, weakly Lindel\

MSC numbers: 54G05, 54C10, 54D20