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We revisit a well-known "surjectivity onto quotient" type lemma of Kirchbergon the central sequence algebra of a separable unital ${\rm C}^*$-algebra, anduse it to prove a "surjectivity onto quotient" result on approximately innerautomorphisms of a separable unital ${\rm C}^*$-algebra of stable rank one,which we can partially upgrade also to the non-separable case.

An application of Kirchberg's lemma on central sequence algebras to groups of approximately inner automorphisms