- quotient topology
- мат.фактор-топология
English-Russian scientific dictionary. 2008.
quotient topology
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Quotient space — In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. The points to be identified are specified … Wikipedia
Quotient space (linear algebra) — In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by collapsing N to zero. The space obtained is called a quotient space and is denoted V / N (read V mod N ). Definition Formally, the construction is… … Wikipedia
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Natural topology — In any domain of mathematics, a space has a natural topology if there is a topology on the space which is best adapted to its study within the domain in question. In many cases this imprecise definition means little more than the assertion that… … Wikipedia
Final topology — In general topology and related areas of mathematics, the final topology (inductive topology or strong topology) on a set X, with respect to a family of functions into X, is the finest topology on X which makes those functions continuous.… … Wikipedia
Cone (topology) — Cone of a circle. The original space is in blue, and the collapsed end point is in green. In topology, especially algebraic topology, the cone CX of a topological space X is the quotient space: of the … Wikipedia
Continuous function (topology) — In topology and related areas of mathematics a continuous function is a morphism between topological spaces. Intuitively, this is a function f where a set of points near f(x) always contain the image of a set of points near x . For a general… … Wikipedia
Disjoint union (topology) — In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the… … Wikipedia
Coherent topology — In topology, a coherent topology is one that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. Contents 1 Definition 2… … Wikipedia
List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability … Wikipedia
Suspension (topology) — In topology, the suspension SX of a topological space X is the quotient space::SX = (X imes I)/{(x 1,0)sim(x 2,0)mbox{ and }(x 1,1)sim(x 2,1) mbox{ for all } x 1,x 2 in X}of the product of X with the unit interval I = [0, 1] . Intuitively, we… … Wikipedia
