Journal of the
Korean Mathematical Society JKMS

Observing that for any $\beta_c$-Wallman functor $\Cal A$ and any Tychonoff space X, there is a cover (C$_1(\Cal A$(X), X), $c_1$) of X such that X is $\Cal A$-disconnected if and only if $c_1$ : C$_1(\Cal A$(X), X) $\longrightarrow$ X is a homeomorphism, we show that every Tychonoff space has the minimal $\Cal A$-disconnected cover. We also show that if X is a weakly Lindel\" of or locally compact zero-dimensional space, then the minimal G-disconnected (equivalently, cloz)-cover is given by the space C$_1(\Cal A$(X), X) which is a dense subspace of E$_{cc}$($\beta$X).

Keywords: covering map, $\Cal A$-disconnected space, minimal cover

MSC numbers: 54C10, 54D80, 54G05