On a complex collar neighbourhood theorem

Abstract

The purpose of this note is to review the complex collar neighbourhood theorem of our paper [6] and add an extra precision to its proof. This is motivated by the importance of the subject, which attracted the attention of several authors, (see e.g. [2, 3, 4]). The two main ingredients consist of a local extension (or realizability) result (see [5]) and an ingenious use of the Zorn lemma which, in the non-compact case, is a substitute for the bumping technique of [1]. Our result is the following.