**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 A group cum topological space whose group operations are continuous functions … Wiktionary

**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