In this article, we extend some results of infinitesimal analysis on normed spaces and the field of reals to the functional representation of a Boolean-valued universe. In particular, we prove equivalence of the following three conditions for an arbitrary polyverse over Q: a point q ϵ Q is not σ-isolated; the stalk of the polyverse at q is countably saturated; and the nonstandard hull of every normed space in the stalk of the polyverse at q is complete.

Keywords:Boolean-valued analysis, infinitesimal analysis, nonstandard analysis, polyverse, nonstandard hull.