Mixed topological groups (Q807754)

Let \(T_ 1\) and \(T_ 2\) be two group topologies on a group G. The family of \(T_ 1\)-closures of \(T_ 2\)-neighbourhoods of the identity e in G is a base for e in a unique topology \(T_ 1(T_ 2)\) on G such that \((G,T_ 1(T_ 2))\) is a topological group - a mixed topological group. The authors prove a few simple structural properties of a mixed topological group.