Minimal basically disconnected covers of product spaces

Abstract

In this paper, we show that if the minimal basically disconnectedcover Lambda X_i of X_i is given by the space of fixedsigma Z(X)^#-ultrafilters on X_i (i = 1, 2) and LambdaX_1 times Lambda X_2 is a basically disconnected space,then Lambda X_1 times Lambda X_2 is the minimal basicallydisconnected cover of X_1times X_2. Moreover, observing thatthe product space of a P-space and a countably locally weaklyLindel" of basically disconnected space is basicallydisconnected, we show that if X is a weakly Lindel" of almostP-space and Y is a countably locally weakly Lindel" of space,then (Lambda X times Lambda Y, Lambda_X timesLambda_Y) is the minimal basically disconnected cover of Xtimes Y.