Open mapping theorem
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.
See also
- In calculus, part of the inverse function theorem which states that a continuously differentiable function between Euclidean spaces whose derivative matrix is invertible at a point is an open mapping in a neighborhood of the point. More generally, if a mapping F : U → Rm from an open set U ⊂ Rn to Rm is such that the Jacobian derivative dF(x) is surjective at every point x ∈ U, then F is an open mapping.
- The invariance of domain theorem shows that certain mappings between subsets of Rn are open.
This set index article includes a list of related items that share the same name (or similar names).
If an internal link incorrectly led you here, you may wish to change the link to point directly to the intended article.
If an internal link incorrectly led you here, you may wish to change the link to point directly to the intended article.
Content Disclaimer
Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.
- The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
- There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
- It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
- Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
- Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.