Bornologies and Lipschitz analysis. (2023)
- Record Type:
- Book
- Title:
- Bornologies and Lipschitz analysis. (2023)
- Main Title:
- Bornologies and Lipschitz analysis
- Further Information:
- Note: Gerald Beer.
- Authors:
- Beer, Gerald Alan
- Contents:
- Background material. Continuous functions on metric spaces. Extension of real-valued continuous functions on subsets of a metric space. The Arens-Eells theorem and the Hausdorff extension theorem. Nets and uniformities. Some basic bornologies. Total boundedness revisited and Bourbaki boundedness. Localy Lipschitz functions. Common sets of boundedness for classes of continuous functions. Hejcman’s theorem and its analog for totally bounded subsets. General constructions with bornologies. Properties of bornologies. Approximation by members of a bornology. Selected topological properties of the one-point extension. Bornologies of metrically bounded sets. Bornologies of totally bounded sets. Strong uniform continuity. UC-subsets. UC-spaces. Pointwise products of uniformly continuous real-valued functions. Strong uniform convergence on bornologies. Uniform convergence on totally bounded subsets. Where must each member of a class of locally Lipschitz functions be Lipschitz? Real-valued Lipschitz functions and classes of locally Lipschitz functions. Coarse maps on metrically convex spaces. Some density results. More on our 4 classes of locally Lipschitz functions. Real-valued functionals and bornologies. Uniformly paracompact subsets. Uniformly paracompact spaces and uniformly locally Lipschitz functions. Bornological convergence of nets of closed subsets. Attouch-Wets convergence. Topologies of uniform convergence on B (X, Y) and convergence of graphs. Bornological convergence andBackground material. Continuous functions on metric spaces. Extension of real-valued continuous functions on subsets of a metric space. The Arens-Eells theorem and the Hausdorff extension theorem. Nets and uniformities. Some basic bornologies. Total boundedness revisited and Bourbaki boundedness. Localy Lipschitz functions. Common sets of boundedness for classes of continuous functions. Hejcman’s theorem and its analog for totally bounded subsets. General constructions with bornologies. Properties of bornologies. Approximation by members of a bornology. Selected topological properties of the one-point extension. Bornologies of metrically bounded sets. Bornologies of totally bounded sets. Strong uniform continuity. UC-subsets. UC-spaces. Pointwise products of uniformly continuous real-valued functions. Strong uniform convergence on bornologies. Uniform convergence on totally bounded subsets. Where must each member of a class of locally Lipschitz functions be Lipschitz? Real-valued Lipschitz functions and classes of locally Lipschitz functions. Coarse maps on metrically convex spaces. Some density results. More on our 4 classes of locally Lipschitz functions. Real-valued functionals and bornologies. Uniformly paracompact subsets. Uniformly paracompact spaces and uniformly locally Lipschitz functions. Bornological convergence of nets of closed subsets. Attouch-Wets convergence. Topologies of uniform convergence on B (X, Y) and convergence of graphs. Bornological convergence and uniform convergence of distance functionals. Bornological convergence with respect to the compact bornology. When is bornological convergence topological? Uniformizability and metrizability. Ideals, bornologies and extensions. When is an extension bornological? … (more)
- Edition:
- 1st
- Publisher Details:
- Boca Raton : CRC Press
- Publication Date:
- 2023
- Extent:
- 1 online resource (232 pages)
- Subjects:
- 515.73
Bornological spaces
Lipschitz spaces - Languages:
- English
- ISBNs:
- 9781000884302
9781000884364 - Related ISBNs:
- 9780367497873
- Notes:
- Note: Includes bibliographical references and index.
Note: Description based on CIP data; resource not viewed. - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.764130
- Ingest File:
- 18_057.xml