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The extending topologies 
International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 621-623
http://dx.doi.org/10.1155/S0161171284000673

The extending topologies

Bradd Clark and Victor Schneider

Department of Mathematics and Statistics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USA

Received 14 December 1983

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let H be a topological group and a subgroup of G . A topology on G is called an extending topology if and only if it makes G a topological group and it induces the given topology on H . The set of all such topologies is studied.