In their paper (l) on the general theory of connectednesses and disconnectednesses, Arhangel'skiĭ and Wiegandt conclude by proposing several problems. We shall show in this note, by elementary constructions (assuming of course the axiom of choice), that the answer to their questions (d) and (e) is negative in both cases; we also consider a modified form of question (d) to which the answer is positive. Our notation is that of (l) and references, unless otherwise stated, are to that paper; thus ‘(1·3)’ means ‘Proposition 1·3 of (l)’, but ‘(2·1 above)’ means ‘Proposition 2·1 of the present note.’