We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.

We show the uniqueness of minimal actions of a compact Kac algebra with the amenable dual on the AFD factor of type II1. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.

We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the CuntzKrieger uniqueness theorem, and compute the K-groups of our algebras.

The purpose of this note is to state a collection of results, all related to questions of uniqueness of smooth neighborhoods of finite complexes as imbedded (nicely) in differentiable manifolds. The reported results will appear in subsequent papers, the first of which is [l ]. The approach taken is always via the theory of simple homotopy types (due to J. H. C. Whitehead), and the main theorem ...

Of course, the answer to the question posed in the title is no, in general, but, surprisingly enough, yes in a significant situation to be detailed later. This paper aims to bring to the attention of the widest possible mathematical audience an elementary result, based on the theorem of differentiation of inverse functions, which extends the applicability of uniqueness theorems. Loosely speakin...