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

Learn More About topological group

Time Traveler for topological group

Time Traveler

The first known use of topological group was in 1946

See more words from the same year

Dictionary Entries Near topological group

topological equivalence

topological group

topologically equivalent

See More Nearby Entries 

Statistics for topological group

Cite this Entry

“Topological group.” Dictionary, Merriam-Webster, Accessed 23 Jan. 2022.

Style: MLA
MLACheck Mark Icon ChicagoCheck Mark Icon APACheck Mark Icon Merriam-WebsterCheck Mark Icon

More from Merriam-Webster on topological group Encyclopedia article about topological group


Test Your Vocabulary

Difficult Spelling Words Quiz

  • alphabet pasta spelling help
  • Which is the correct spelling?
Spell It

Can you spell these 10 commonly misspelled words?

Universal Daily Crossword

A daily challenge for crossword fanatics.

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!