The completeness problem for maximal topological groups
A topological group G is maximal if its topology is maximal in the set of all non-discrete group topologies on G. The question of the existence of maximal non-complete topological groups is considered. One can prove that under CH every infinite abelian group admits a complete maximal group topology. Using the Booth Lemma, the authors construct: (1) a complete maximal group G whose topology is the supremum of an increasing \(2^{\omega}\)-sequence of non-discrete linear metrizable topologies on G (Example 2.2); (2) a non-complete maximal topological group (Example 3.3). The completeness of some topological groups which are close to maximal ones is also considered.
scientific article; zbMATH DE number 4208398