The object of this paper is to
study analytic continuation of algebras of functions holomorphic on complex spaces
of dimension greater than 1. Classically this has been done by putting complex
structure on the maximal spectrum of the algebra so that the spectrum is a
Stein space with respect to the induced algebra of holomorphic functions.
Grauert has given non-pathological examples where this is not possible. In the
present paper the axioms of a Stein space have been weakened and the weak
envelope of holomorphy has been constructed for a certain type of algebra. In
particular, if the algebra A separates points and gives local coordinates on a
complex space X then the weak envelope of holomorphy for the pair, (X,A) is
obtained.
