TOPOLOGICAL GROUP

[topological group] n (1946): a mathematical group which is also a topological space, whose multiplicative operation is continuous such that given any neighborhood of a product there exist neighborhoods of the elements composing the product with the property that any pair of elements representing each of these neighborhoods form a product belonging to the given neighborhood, and whose operation of taking inverses is continuous such 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