topological group


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

1946, in the meaning defined above

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The first known use of topological group was in 1946

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Cite this Entry

“Topological group.” Dictionary, Merriam-Webster, Accessed 4 Dec. 2020.

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