topological group

topological group
A group-cum-topological space whose group operations are continuous functions.

Wikipedia foundation.

Look at other dictionaries:

• Topological group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• topological group — noun : 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… …   Useful english dictionary

• topological group — Math. a set that is a group and a topological space and for which the group operation and the map of an element to its inverse are continuous functions. [1945 50] * * * …   Universalium

• topological group — noun Date: 1946 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 …   New Collegiate Dictionary

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …   Wikipedia

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Topological ring — In mathematics, a topological ring is a ring R which is also a topological space such that both the addition and the multiplication are continuous as maps : R times; R → R ,where R times; R carries the product topology. General comments The group …   Wikipedia

• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

• Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   Wikipedia