Let M be a von Neumann algebra with a cyclic and separating vector ξ0 and J# (resp. Jb) be the closure of M+ξ0 (resp. M′+ξ0). It is shown that the map: ξ∈J#→ωξ∈M+* is a homeomorphism with respect to the norm topologies. It is also shown that J# can be replaced by Jb if M is finite.