Rapley, William Henry
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The purpose of this paper is to introduce the reader to the field of topological groups. - In the first two sections, we list definitions and theorems from topology and group theory which are used in proving the results about topological groups that we obtain in sections ITI and IV. - Section III deals with the results of our general knowledge in the field of topological groups. - Section IV shows how we can increase Our knowledge of topological. groups by relating certain topological transformation groups such as character groups to a general topological group. The structure of this paper is based on the method of L. Pontrjagin, in his book Topological groups.