Resolvable, not maximally resolvable spaces

AbstractThe formation of maximal topologies and the use of maximal independent families are the only known techniques for constructing irresolvable spaces. Using side conditions to control maximal constructions, we give a new construction of n-resolvable, not (n + 1)-resolvable spaces. In another direction, we use the existence of a crowded, irresolvable, strong Pκ space to construct infinitely resolvable, not maximally resolvable spaces. Relative to the existence of a measurable cardinal, the latter result answers several longstanding questions in this area