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Inverse Images Of Generalized Metric Spaces Under Closed Maps
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Book Synopsis Generalized Metric Spaces and Mappings by : Shou Lin
Download or read book Generalized Metric Spaces and Mappings written by Shou Lin and published by Springer. This book was released on 2016-10-20 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.
Book Synopsis Introduction to Metric and Topological Spaces by : Wilson A Sutherland
Download or read book Introduction to Metric and Topological Spaces written by Wilson A Sutherland and published by Oxford University Press. This book was released on 2009-06-18 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Book Synopsis Topics in General Topology by : K. Morita
Download or read book Topics in General Topology written by K. Morita and published by Elsevier. This book was released on 1989-08-04 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
Book Synopsis Studies in Topology by : Nick M. Stavrakas
Download or read book Studies in Topology written by Nick M. Stavrakas and published by Academic Press. This book was released on 2014-05-10 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Symposia Mathematica written by and published by . This book was released on 1975 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-11-11 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Calculus of Variations and Optimal Control Theory by : Laurence Chisholm Young
Download or read book Lectures on the Calculus of Variations and Optimal Control Theory written by Laurence Chisholm Young and published by American Mathematical Soc.. This book was released on 2000 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.
Book Synopsis General Topology III by : A. V. Arhangel' skii
Download or read book General Topology III written by A. V. Arhangel' skii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.
Book Synopsis Encyclopaedia of Mathematics (set) by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics (set) written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Book Synopsis Functional Analysis by : L. V. Kantorovich
Download or read book Functional Analysis written by L. V. Kantorovich and published by Elsevier. This book was released on 2016-02-16 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis, Second Edition is an exposition of the theory of topological vector spaces, partially ordered spaces, and the development of the theory of integral operators and their representations on ideal spaces of measurable functions. Although this edition has deviated substantially from the first edition, it has still retained the overall plan, selection, and arrangement of the topics. The text is primarily devoted to the applications of functional analysis to applied analysis. However, these concepts have been extended and modernized. Some topics of functional analysis connected with applications to mathematical economics and control theory are also included in this edition. The applications of functional analysis are both wide and far-reaching as these are common language for all areas of mathematics involving the concept of continuity. Those who are in the field of mathematics, mechanics, and theoretical physics will find this book a valuable resource.
Book Synopsis Elements of the Theory of Functions and Functional Analysis by : Andre? Nikolaevich Kolmogorov
Download or read book Elements of the Theory of Functions and Functional Analysis written by Andre? Nikolaevich Kolmogorov and published by Courier Corporation. This book was released on 1999-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
Book Synopsis Elements of the Theory of Functions and Functional Analysis by : Andreĭ Nikolaevich Kolmogorov
Download or read book Elements of the Theory of Functions and Functional Analysis written by Andreĭ Nikolaevich Kolmogorov and published by Courier Corporation. This book was released on 1957 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Notices of the American Mathematical Society by : American Mathematical Society
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1974 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles of significant interest to mathematicians, including reports on current mathematical research.
Book Synopsis Lectures on Coarse Geometry by : John Roe
Download or read book Lectures on Coarse Geometry written by John Roe and published by American Mathematical Soc.. This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
Download or read book Rozprawy Matematyczne written by and published by . This book was released on 1977 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Topology and Its Relations to Modern Analysis and Algebra 2 by : Z. Frolík
Download or read book General Topology and Its Relations to Modern Analysis and Algebra 2 written by Z. Frolík and published by Academic Press. This book was released on 2014-05-12 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.
