topological group

noun

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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Dictionary Entries Near topological group

topological equivalence

topological group

topologically equivalent

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Cite this Entry

“Topological group.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/topological%20group. Accessed 23 Jan. 2022.

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More from Merriam-Webster on topological group

Britannica.com: Encyclopedia article about topological group

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