Open mappings of locally compact groups (Q6634491)

This concise, well-motivated note aims to (in the authors' words) ``insert in the literature some [\dots] not widely known'' open mapping-type theorems for locally compact groups. The main results are the following:\N\N(Theorem 2) Let \(G\) and \(H\) be locally compact groups and \(\phi:G\to H\) a continuous homomorphism. If \(\phi\) transforms open subgroups of \(G\) into open subgroups of \(H\), then \(\phi\) is an open mapping.\N\N(Corollary 8) Let \(G\) and \(H\) be locally compact groups and \(\phi:G\to H\) a continuous homomorphism. If there exists a compact subset \(K\) of \(G\) such that \(\phi(K)\) has positive Haar measure, then \(\phi\) is an open mapping.