We show that the Niemytzki plane, which is connected Tychonoff, is not resolvable.This addresses a question raised by Comfort as to whether a concrete example of an irresolvable connected Tychonoff without isolated points exists. To demonstrate the case we present the following results: (a) A resolvable Cech-complete contains a dense Cech-complete subspace whose complement is dense.\\ (b) A resolvable space contains some infinite subsets whose derived sets are not empty. (c) Necessary and sufficient conditions of resolvability and irresolvability are also given.