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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.

Perturbations of intermediate C∗‐subalgebras for simple C∗‐algebras