Let $N$ be a normal subgroup of a path-connected topological group $(G,t)$. In this paper, the authors consider the existence of path-connectedness in refined topologies in order to address the property of maximal path-connectedness in topological groups. In particular, refinements on $t$ and refinements on the quotient topology on $G/N$ are studied. The preservation of path-connectedness in extending topologies and translation topologies is also considered.

Keywords: topological group, path-connected, normal subgroup, extending topologies