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Keywords:
maximal n.d. set; $P$-set; maximal n.d. $P$-set; compact space; basically disconnected space; $F$-space
maximal n.d. set; $P$-set; maximal n.d. $P$-set; compact space; basically disconnected space; $F$-space
Summary:
In [5] the following question was put: are there any maximal n.d. sets in $\omega^*$? Already in [9] the negative answer (under {\bf MA}) to this question was obtained. Moreover, in [9] it was shown that no $P$-set can be maximal n.d. In the present paper the notion of a maximal n.d. $P$-set is introduced and it is proved that under {\bf CH} there is no such a set in $\omega^*$. The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. $P$-sets in basically disconnected compact spaces with rich families of n.d. $P$-sets is actually solved.
References:
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