最近，Dawson和Feinstein證明了一個交換的Banach代數的拓樸穩定秩是一的話，那它的 Banach 代數整擴張的拓樸穩定秩也是一。在這篇論文中，我們提供了這個命題的部分相反結果：如果一個交換的C*-代數的某個Arens-Hoffman擴張的拓樸穩定秩是一的話，那這個C*-代數的拓樸穩定秩也是一。

Recently, Dawson and Feinstein showed that a Banach algebra integral extension B of a commutative
Banach algebra A of topological stable rank one is again of topological stable rank
one. In this thesis, we provide a partial converse to this statement: If an Arens-Hoffman extension
A® of a commutative C*-algebra A has topological stable rank one then A has topological
stable rank one.

Chapter 1: Introduction 1
Chapter 2: History and definition of dimensions 3
2.1 Historial remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Covering dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Topological stable ranks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3: Results 11
3.1 Notations and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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