Free products of topological groups with amalgamation. II (Q1073925)

Let F and G be topological groups with common subgroup C. If there is a topological group F *\({}_ C G\) such that F and G are topological subgroups of it, \(F\cup G\) generates it algebraically, and every pair of continuous morphisms \(\phi_ 1: F\to D\) and \(\phi_ 2: G\to D\) which agree on C extend to a continuous morphism of F *\({}_ C G\) into D, then F *\({}_ C G\) is called the free product of F and G with amalgamated subgroup C. The fundamental problem is to determine if such a product exists and is Hausdorff when F and G are Hausdorff. In an earlier paper [see ibid. 119, 169-180 (1985; Zbl 0581.22002)], the authors proved that this is true if all groups concerned are \(k_{\omega}\) and C is compact. Here they extend that result to cases where C is not compact - for example, if C is the product of a compact subgroup and a subgroup central in F and G. The word beseder is introduced here for a technical property that a triple (F,G,C) may have, and which implies that F *\({}_ C G\) does exist and is Hausdorff. ''Beseder'' is a Hebrew word for ''ok.''