Topological Structures for a Space of Continuous Functions
Author: Richard Eugene McGill
Publisher:
Published: 1958
Total Pages: 68
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Richard Eugene McGill
Publisher:
Published: 1958
Total Pages: 68
ISBN-13:
DOWNLOAD EBOOKAuthor: Richard Eugene McGill
Publisher:
Published: 1959
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert A. McCoy
Publisher: Springer
Published: 2006-12-08
Total Pages: 128
ISBN-13: 3540391819
DOWNLOAD EBOOKThis book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies studied are the set-open topologies and the uniform topologies. Where appropriate, the analogous theorems for the two major classes of topologies are studied together, so that a comparison can be made. A chapter on cardinal functions puts characterizations of a number of topological properties of function spaces into a more general setting: some of these results are new, others are generalizations of known theorems. Excercises are included at the end of each chapter, covering other kinds of function space topologies. Thus the book should be appropriate for use in a classroom setting as well as for functional analysis and general topology. The only background needed is some basic knowledge of general topology.
Author: G.L.M. Groenewegen
Publisher: Springer
Published: 2016-06-17
Total Pages: 183
ISBN-13: 9462392013
DOWNLOAD EBOOKThe space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
Author: Jürgen Flachsmeyer
Publisher:
Published: 1969
Total Pages: 290
ISBN-13:
DOWNLOAD EBOOKAuthor: Wolfgang J. Thron
Publisher:
Published: 1966
Total Pages: 264
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert A. McCoy
Publisher: Springer
Published: 2018-04-21
Total Pages: 121
ISBN-13: 3319770543
DOWNLOAD EBOOKThis book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.
Author: Peter W. Michor
Publisher:
Published: 1980
Total Pages: 176
ISBN-13:
DOWNLOAD EBOOKAuthor: Gerhard Preuß
Publisher: Springer Science & Business Media
Published: 2011-06-27
Total Pages: 306
ISBN-13: 9401004897
DOWNLOAD EBOOKA new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this setting semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, e.g. simple convergence, continuous convergence and uniform convergence. Various interesting results are presented which cannot be obtained by using topological or uniform spaces in the usual context. The text is self-contained with the exception of the last chapter, where the intuitive concept of nearness is incorporated in Convenient Topology (there exist already excellent expositions on nearness spaces).
Author: Leonard Gillman
Publisher: Courier Dover Publications
Published: 2018-01-16
Total Pages: 321
ISBN-13: 0486816885
DOWNLOAD EBOOKDesigned as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.