New Collegiate Dictionary. 2001.
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
topological space — Math. a set with a collection of subsets or open sets satisfying the properties that the union of open sets is an open set, the intersection of two open sets is an open set, and the given set and the empty set are open sets. [1945 50] * * *… … Universalium
topological space — noun (mathematics) any set of points that satisfy a set of postulates of some kind assume that the topological space is finite dimensional • Syn: ↑mathematical space • Topics: ↑mathematics, ↑math, ↑maths … Useful english dictionary
topological space — noun a) A set, together with a collection of its subsets that form a topology on the set. b) The set itself … Wiktionary
Finite topological space — In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space for which there are only finitely many points.While topology is mostly interesting only for… … Wikipedia
Noetherian topological space — In mathematics, a Noetherian topological space is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the… … Wikipedia
Localization of a topological space — In mathematics, well behaved topological spaces can be localized at primes, in a similar way to the localization of a ring at a prime. This construction was described by Dennis Sullivan in 1970 lecture notes that were finally published in… … Wikipedia
Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… … Wikipedia
Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… … Wikipedia
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
