Encyclopedia
Open mapping theorem
Index of articles associated with the same name
Open mapping theorem may refer to:
- Open mapping theorem (functional analysis) (also known as the 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.
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This article is adapted from the Wikipedia article “Open mapping theorem”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
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