Perturbations of intermediate C*-subalgebras for simple C*-algebras

We study uniform perturbations of intermediate C-subalgebras of inclusions of simple C-algebras. If a unital simple C-algebra has a simple C-subalgebra of finite index, then sufficiently close intermediate C-subalgebras are unitarily equivalent. These intermediate C-subalgebras need not be nuclear. The unitary can be chosen in the relative commutant algebra. An immediate corollary is the following: If the relative commutant is trivial, then the set of intermediate C-subalgebras is a finite set.