Definition of topological group
: a mathematical group which is also a topological space, whose multiplicative operation has the property that given any neighborhood of a product there exist neighborhoods of the elements composing the product such that any pair of elements representing each of these neighborhoods form a product belonging to the given neighborhood, and whose operation of taking inverses has the property that for any neighborhood of the inverse of an element there exists a neighborhood of the element itself in which every element has its inverse in the other neighborhood
First Known Use of topological group
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Britannica.com: Encyclopedia article about "topological group"
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