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) states that a non-constant holomorphic function on a connected open set in the complex plane is an open mapping
- Open mapping theorem (topological groups) states that a surjective continuous homomorphism of a locally compact Hausdorff group G onto a locally compact Hausdorff group H is an open mapping if G is σ-compact. Like the open mapping theorem in functional analysis, the proof in the setting of topological groups uses the Baire category theorem.
Famous quotes containing the words open and/or theorem:
“Philosophy is written in this grand book—I mean the universe—
which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.”
—Galileo Galilei (1564–1642)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)