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Topological Properties Of Spaces Of Continuous Functions
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Book Synopsis Topological Properties of Spaces of Continuous Functions by : Robert A. McCoy
Download or read book Topological Properties of Spaces of Continuous Functions written by Robert A. McCoy and published by Springer. This book was released on 2006-12-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Book Synopsis Topological Properties of Spaces of Continuous Functions by : Robert A. McCoy
Download or read book Topological Properties of Spaces of Continuous Functions written by Robert A. McCoy and published by . This book was released on 2014-01-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Properties of the Standard Operations on Spaces of Continuous Functions and Integrable Functions by : Holly Michelle Renaud
Download or read book Topological Properties of the Standard Operations on Spaces of Continuous Functions and Integrable Functions written by Holly Michelle Renaud and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we consider different notions of openness for several operations on a large collection of different settings. We start with the scalar multiplication on sequence spaces, spaces of continuous functions, and integrable functions. We apply different techniques to derive weak-openness of multiplication on spaces of differentiable functions, endowed with a large collection of quasi-algebra norms. We consider the openness property of the dense-defined standard multiplication on spaces of integrable functions, as multiplication on these settings is only defined on a dense set. We adapt the definition of openness for the multiplication to include dense-defined products and then prove that the multiplication on these spaces, restricted to their corresponding domains, is uniformly open. We investigate sufficient and necessary conditions for pairs of functions to be points of local openness for the multiplication on normed spaces of differentiable functions. Next, we establish openness for other kinds of operations, more precisely, the maximum and minimum operations on spaces of scalar-valued integrable functions from a topological space into a finite measure on an algebra of subsets of that space. The last section of this work deals with the connection between openness of the multiplication on spaces of continuous functions and topological properties of the domain of those functions..
Book Synopsis Topological Structures for a Space of Continuous Functions by : Richard Eugene McGill
Download or read book Topological Structures for a Space of Continuous Functions written by Richard Eugene McGill and published by . This book was released on 1958 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Descriptive Topology in Selected Topics of Functional Analysis by : Jerzy Kąkol
Download or read book Descriptive Topology in Selected Topics of Functional Analysis written by Jerzy Kąkol and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.
Book Synopsis Set-Valued Mappings, Selections and Topological Properties of 2x by : W. M. Fleischman
Download or read book Set-Valued Mappings, Selections and Topological Properties of 2x written by W. M. Fleischman and published by Springer. This book was released on 2006-11-15 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Function Spaces with Uniform, Fine and Graph Topologies by : Robert A. McCoy
Download or read book Function Spaces with Uniform, Fine and Graph Topologies written by Robert A. McCoy and published by Springer. This book was released on 2018-04-21 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Book Synopsis Rings of Continuous Functions by : L. Gillman
Download or read book Rings of Continuous Functions written by L. Gillman and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to those who know the meaning of each word in the title: none is defined in the text. The reader can estimate the knowledge required by looking at Chapter 0; he should not be dis couraged, however, if he finds some of its material unfamiliar or the presentation rather hurried. Our objective is a systematic study of the ring C(X) of all real-valued continuous functions on an arbitrary topological space X. We are con cerned with algebraic properties of C(X) and its subring C*(X) of bounded functions and with the interplay between these properties and the topology of the space X on which the functions are defined. Major emphasis is placed on the study of ideals, especially maximal ideals, and on their associated residue class rings. Problems of extending continuous functions from a subspace to the entire space arise as a necessary adjunct to this study and are dealt with in considerable detail. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5 and the beginning of Chapter 10, presents the fundamental aspects of the subject insofar as they can be discussed without introducing the Stone-Cech compactification. In Chapter 3, the study is reduced to the case of completely regular spaces.
Book Synopsis Recent Progress in Function Spaces by : Giuseppe Di Maio
Download or read book Recent Progress in Function Spaces written by Giuseppe Di Maio and published by . This book was released on 1998 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Basic Topology 1 by : Avishek Adhikari
Download or read book Basic Topology 1 written by Avishek Adhikari and published by Springer Nature. This book was released on 2022-07-04 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
Download or read book Topology and Maps written by T. Husain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).
Book Synopsis Pseudocompact Topological Spaces by : Michael Hrušák
Download or read book Pseudocompact Topological Spaces written by Michael Hrušák and published by Springer. This book was released on 2018-07-19 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.
Book Synopsis Non-Hausdorff Topology and Domain Theory by : Jean Goubault-Larrecq
Download or read book Non-Hausdorff Topology and Domain Theory written by Jean Goubault-Larrecq and published by Cambridge University Press. This book was released on 2013-03-28 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
Download or read book Topology written by and published by Academic Press. This book was released on 1966-01-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology
Book Synopsis Topological Spaces by : Claude Berge
Download or read book Topological Spaces written by Claude Berge and published by Courier Corporation. This book was released on 1997-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
Book Synopsis Topology Essentials by : Emil G. Milewski
Download or read book Topology Essentials written by Emil G. Milewski and published by Research & Education Assoc.. This book was released on 2013-01-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, countable spaces, and separation axioms.
Download or read book Topological Algebras written by and published by Elsevier. This book was released on 2011-10-10 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Cech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
