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open-closed subset

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  • 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

  • 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

  • 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

  • Open source software security — is the measure of assurance or guarantee in the freedom from danger and risk inherent to an open source software system. Contents 1 The debate 1.1 Benefits of open source security 1.2 Drawbacks of open source security …   Wikipedia

  • Open standard — An open standard is a standard that is publicly available and has various rights to use associated with it, and may also have various properties of how it was designed (e.g. open process). There is no single definition and interpretations vary… …   Wikipedia

  • Open mapping theorem (complex analysis) — In complex analysis, the open mapping theorem states that if U is a connected open subset of the complex plane C and f : U → C is a non constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of… …   Wikipedia

  • Closed world assumption — The closed world assumption (CWA) is the presumption that what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed world assumption is… …   Wikipedia

  • Open sentence — In mathematics, an open sentence (usually an equation or equality) is described as open in the sense that its truth value is meaningless until its variables are replaced with specific numbers, at which point the truth value can usually be… …   Wikipedia

  • 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

  • closed — adjective Date: 13th century 1. a. not open b. enclosed c. composed entirely of closed tubes or vessels < a closed circulatory system > 2. a. forming a self contained unit allowing no additions …   New Collegiate Dictionary

  • Open format — An open file format is a published specification for storing digital data, usually maintained by a standards organization, which can therefore be used and implemented by anyone. For example, an open format can be implementable by both proprietary …   Wikipedia

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