Principles Of Topology

Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 9780486801544
Size: 15.32 MB
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Designed for a one-semester introductory course, this text covers metric spaces, general topological spaces, continuity, topological equivalence, basis and subbasis, connectedness and compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. 1989 edition.

Variational Principles Of Topology

Author: A.T. Fomenko
Publisher: Springer
ISBN: 9401073279
Size: 10.26 MB
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One service mathematics has rendered the 'Eot moi, ... , si j'avait JU comment en revenir. human race. h has put common sense back je n'y serais point aUe:' Jules Verne where it belongs, 011 the topmost shelf nen to the dusty canister labeUed 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. H es viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Principles Of Topology

Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 9780486810447
Size: 15.61 MB
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Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.

Principles Of Topology

Author: Fred H. Croom
Publisher: Thomson Learning Asia
ISBN: 9812432884
Size: 11.49 MB
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This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text. Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets. This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus.

Principles Of Topological Psychology

Author: Kurt Lewin
Publisher: Read Books Ltd
ISBN: 9781446547137
Size: 19.48 MB
Format: PDF, Kindle
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The concepts which are discussed in the following chapters have been developed and tried out in the course of the last ten years. They are based on both experimental investigations and case histories. In presenting them we are not promulgating a new “system” limited to a specific content, but rather we are describing a “tool,” a set of concepts by means of which one can represent psychological reality. As I see it, the outstanding characteristics of this undertaking are: 1. It tries to build up a framework for the constructive representation and derivation of psychological processes which is logically consistent and at the same time adapted to the special properties of the “psychological life space.” 2. It includes both the characteristics of the environment and of the person. 3. It makes no more assumptions than are required. 4. It proceeds by a method of successive approximation. The concepts developed in the following pages are “operational” in so far as a univocal relation between concepts and observable data is consistently maintained. Although the concepts always extend from the level of phenomena into the level of causal relationships, they are “descriptive” in the sense of Newton’s dictum: Hypotheses non fingo. That is, they express the nature of certain relationships and at the same time avoid that type of “explanation” which is characteristic of speculative theories and which is at present, as it seems to me, a real handicap to our science.

Recent Progress In General Topology Iii

Author: K.P. Hart
Publisher: Springer Science & Business Media
ISBN: 9789462390249
Size: 16.15 MB
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The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Topology For Analysis

Author: Albert Wilansky
Publisher: Courier Corporation
ISBN: 9780486469034
Size: 17.89 MB
Format: PDF
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Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.