On the ``three-space'' problem for locally quasi-convex topological groups
The main result of this paper is the analogue for topological groups of a theorem due to S.~Dierolf which states that there exists a nonlocally convex twisted sum of the locally convex spaces \(X\) and \(Y\) if and only if there exists a nonlocally convex twisted sum of \(X\) and \(\mathbb R\). It reads as follows: Given two abelian locally quasi-convex groups \(H\) and \(G\) there exists a nonlocally quasi-convex extension of \(H\) and \(G\) if and only if there exists a nonlocally quasi-convex extension of the circle group \(S^1\) and \(G\). The proof relies on methods of homological algebra.
scientific article; zbMATH DE number 1462953