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We observe that a recent theorem of Sato, Toms-White-Winter andKirchberg-Rordam also holds for certain nonunital C*-algebras. Namely, we showthat an algebraically simple, separable, nuclear, nonelementary C*-algebra withstrict comparison, whose cone of densely finite traces has as a base a Choquetsimplex with compact, finite dimensional extreme boundary, and which admits acontinuous rank function, tensorially absorbs the Jiang-Su algebra Z.

Z-stability, finite dimensional tracial boundaries and continuous rank functions