Communications of the
Korean Mathematical Society CKMS

Observing that each Tychonoff space X has the minimal basically disconnected cover $(\Lambda$X, $\Lambda_X)$ and the realcompactification $\upsilon$X, we introduce a concept of stable $\sigma$Z(X)$^\#$-ultrafilters and give internal characterizations of Tychonoff spaces X for which $\Lambda(\upsilon$X) = $\upsilon(\Lambda$X).

Keywords: basically disconnected space, realcompact space, filter space, covering map

MSC numbers: 54G05, 54D60, 54D80, 54C10