- closed and open topology
- открыто-замкнутая топология
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closed and open topology
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Closed and exact differential forms — In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form that is the exterior derivative of another … Wikipedia
Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… … Wikipedia
Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… … Wikipedia
topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c … Universalium
Open and closed maps — In topology, an open map is a function between two topological spaces which maps open sets to open sets.[1] That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function… … Wikipedia
Closed set — This article is about the complement of an open set. For a set closed under an operation, see closure (mathematics). For other uses, see Closed (disambiguation). In geometry, topology, and related branches of mathematics, a closed set is a set… … Wikipedia
Boundary (topology) — For a different notion of boundary related to manifolds, see that article. In topology, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S . More formally, it is… … Wikipedia
Differentially closed field — In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959).… … Wikipedia
Closed manifold — See also: Classification of manifolds#Point set In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold.… … Wikipedia
Closed graph theorem — In mathematics, the closed graph theorem is a basic result in functional analysis which characterizes continuous linear operators between Banach spaces in terms of the operator graph. Contents 1 The closed graph theorem 2 Generalization 3 See… … Wikipedia
Open book decomposition — In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3 manifold M into a union of surfaces (necessarily with boundary) and solid tori. Open books have relevance to contact geometry, with a… … Wikipedia
