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

Keep scrolling for more

Learn More about topological group

Statistics for topological group

Look-up Popularity

Time Traveler for topological group

The first known use of topological group was in 1946

See more words from the same year

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

Comments on topological group

What made you want to look up topological group? Please tell us where you read or heard it (including the quote, if possible).


a bell tower

Get Word of the Day daily email!

Test Your Vocabulary

Where in the World? A Quiz

  • peter bruegel tower of babel painting
  • What language does pajama come from?
Spell It

Can you spell these 10 commonly misspelled words?

Bee Cubed

Test Your Knowledge - and learn some interesting things along the way.

Love words? Need even more definitions?

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