**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

**Open Your Eyes (Snow Patrol song)** — Open Your Eyes Single by Snow Patrol from the album Eyes Open Released … Wikipedia

**Open** — may refer to: Contents 1 Philosophy 2 Mathematics 3 Music and media … Wikipedia

**Open mapping theorem** — may refer to: Open mapping theorem (functional analysis) or Banach–Schauder theorem states that a surjective continuous linear transformation of a Banach space X onto a Banach space Y is an open mapping Open mapping theorem (complex analysis)… … Wikipedia

**open** — openly, adv. openness, n. /oh peuhn/, adj. 1. not closed or barred at the time, as a doorway by a door, a window by a sash, or a gateway by a gate: to leave the windows open at night. 2. (of a door, gate, window sash, or the like) set so as to… … Universalium

**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

**open** — I. adjective (opener; openest) Etymology: Middle English, from Old English; akin to Old High German offan open, Old English ūp up Date: before 12th century 1. having no enclosing or confining barrier ; accessible on all or nearly all sides … New Collegiate Dictionary

**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 mapping theorem (functional analysis)** — In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is… … Wikipedia

**open rectangle** — noun A rectangle in the real plane which is an open set: i.e., which does not contain its edges. If the sides of the open rectangle are parallel to the planes axes, then the open rectangle can be described as the Cartesian product of two open… … Wiktionary