Elements of the theory of topological groups
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In this chapter we initiate the program described at the beginning of Chapter One: namely, we define and study the structure of topological groups. Certain refined results in structure theory must be postponed to Chapter Five, where the powerful analytical tool of representation theory will have been made available. It seems appropriate to do at the outset what can be done with one’s bare hands, so to say; and this we will now do. Section 10 contains the description of a few special topological groups which are important for later use; the remainder of the chapter deals with structural properties of one or another class of topological groups.
KeywordsNormal Subgroup Topological Group Compact Group Quotient Group Compact Subgroup
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