# Path-connected Group Extensions

• Edler, Laurie A. (Department of Mathematics, Georgia College & State University) ;
• Schneider, Victor P. (Department of Mathematics, University of Louisiana at Lafayette)
• Received : 2005.05.16
• Published : 2006.09.23

#### Abstract

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.

#### References

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2. L. Edler, Path-connectedness in the plane as a topological group, Int. Math. J., 2(7)(2002), 719-725.
3. M. Tkachenko and L. M. Villegas-Silva, Refining connected topological group topologies on abelian torsion-free groups, J. Pure Appl. Alg., 124(1998), 281-288. https://doi.org/10.1016/S0022-4049(96)00109-0