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For each positive integer n, a o-Z-set B" in the Hilbert cube 7°° is constructed whose complement s" = Ix -B" is not homeomorphic to the pseudointerior j of the Hilbert cube though sn and B" satisfy: (i) every compact subset of s" is a Z-set in s"; (ii) s" X s" is homeomorphic to s; (iii) Bn admits small maps 7°° -» B"; (iv) s" satisfies the discrete «-cells property; and (v) Bn is locally (n -1)connected in /°°. It is shown that sn does not satisfy the discrete (n + l)-cells property and thusdoi:10.1090/s0002-9939-1985-0766541-4 fatcat:wgoq4le33rayrmngwz2brcvyl4