Canonical Extensions of Embeddings in Euclidean Space
Title | Canonical Extensions of Embeddings in Euclidean Space PDF eBook |
Author | David B. Gauld |
Publisher | |
Pages | 18 |
Release | 1974 |
Genre | Embeddings (Mathematics) |
ISBN |
Embeddings and Extensions in Analysis
Title | Embeddings and Extensions in Analysis PDF eBook |
Author | James Howard Wells |
Publisher | Springer |
Pages | 128 |
Release | 1975 |
Genre | Mathematics |
ISBN |
Embeddings and Extensions in Analysis
Title | Embeddings and Extensions in Analysis PDF eBook |
Author | J.H. Wells |
Publisher | Springer Science & Business Media |
Pages | 117 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642660371 |
The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger [1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg [1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun [1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space [1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X,Y) of Banach spaces for which extension of contractions is always possible [1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine [1966].
Axiomization of Passage from `Local' Structure to `Global' Object
Title | Axiomization of Passage from `Local' Structure to `Global' Object PDF eBook |
Author | Paul Feit |
Publisher | American Mathematical Soc. |
Pages | 121 |
Release | 1993 |
Genre | Categories |
ISBN | 0821825461 |
This paper offers a systematic approach to all mathematical theories with local/global behavior. To build objects with local and global aspects, on begins with a category of [script]C of allowed local structures, and somehow derives a category [script]C[superscript]gl of things which are 'locally' in [script]C. Some global objects, such as manifolds or schemes, can be represented as a sheaf of algebras on a topological base space; others, like algebraic spaces, are more technical. These theories share common structure--certain theorems on inverse limits, descent, and dependence on special class of morphism appear in all cases. Yet, classical proofs for universal properties proceed by case-by-case study. Separate examples require distinct arguments.
Nan Shu Xue Xue Bao
Title | Nan Shu Xue Xue Bao PDF eBook |
Author | |
Publisher | |
Pages | 458 |
Release | 1976 |
Genre | Mathematics |
ISBN |
Transactions of the American Mathematical Society
Title | Transactions of the American Mathematical Society PDF eBook |
Author | |
Publisher | |
Pages | 972 |
Release | 1975 |
Genre | Mathematics |
ISBN |
Introduction to Boolean Algebras
Title | Introduction to Boolean Algebras PDF eBook |
Author | Steven Givant |
Publisher | Springer Science & Business Media |
Pages | 589 |
Release | 2008-12-02 |
Genre | Mathematics |
ISBN | 0387402934 |
This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.