Kyungpook Mathematical Journal 2006; 46(3): 445-448
Published online September 23, 2006
Copyright © Kyungpook Mathematical Journal.
Path-connected Group Extensions
Laurie A. Edler1, Victor P. Schneider2
1Department of Mathematics, Georgia College & State University, Milledgeville, GA 31061, U.S.A.
2Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, U.S.A.
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