A note on resolvability

A topological space is said to be resolvable if it has two disjoint dense subsets. If ℵ is a cardinal number(finite or infinite), a topological space is said to be ℵ -resolvable if it has a paiwise disjoint family of ℵ many dense subsets. Illanes [ 3 ] showed that a topological space which is κ -resolvable for every finite integer κ is necessarily ℵ 0 -resolvable. We generalize this result to infinite cardinals. We show that if a topological space X is κ -resolvable for every κ < ℵ and if cofinality of ℵ is ℵ 0 , then, X is ℵ -resolvable.