A.V. Koldunov, A.I. Veksler
Maximal nowhere dense P-sets in basically disconnected spaces and F-spaces

Comment.Math.Univ.Carolinae 42,2 (2001) 363-378.

Abstract:In [5] the following question was put: are there any maximal n.d. sets in $\omega ^*$? Already in [9] the negative answer (under {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 {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.

Keywords: maximal n.d. set, $P$-set, maximal n.d. $P$-set, compact space, basically disconnected space, $F$-space
AMS Subject Classification: 54B05, 54G05, 54D30, 54D40