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Minimal basically disconnected covers of some extensions

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Abstract

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).

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