Principles Of Topology

Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 9780486801544
Size: 19.27 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.

Principles Of Topology

Author: Fred H. Croom
Publisher: Thomson Learning Asia
ISBN: 9812432884
Size: 20.67 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: 9781447494881
Size: 12.63 MB
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PRINCIPLES OF TOPOLOGICAL PSYCHOLOGY by KURT LEWIN. Originally published in 1936. PREFACE by DR. WOLFGANG KOHLER Swarthmore College Swarthmore: DEAR KOHLER This book is the result of a very slow growth. I remember the moment when more than ten years ago it occurred to me that the figures on the blackboard which were to illustrate some problems for a group in psychology might after all be not merely illustrations but representations of real concepts. Much interested in the theory of science, I had already in 1912 as a student defended the thesis against a then fully accepted philo sophical dictum that psychology, dealing with manifolds of coexist ing facts, would be finally forced to use not only the concept of time but that of space too. Knowing something of the general theory of point sets, I felt vaguely that the young mathematical discipline topology might be of some help in making psychology a real science. I began studying topology and making use of its concepts, which soon appear

Variational Principles Of Topology

Author: A.T. Fomenko
Publisher: Springer
ISBN: 9401073279
Size: 18.30 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.

Recent Progress In General Topology Iii

Author: K.P. Hart
Publisher: Springer Science & Business Media
ISBN: 9789462390249
Size: 15.22 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.

A First Course In Topology

Author: Robert A Conover
Publisher: Courier Corporation
ISBN: 9780486780016
Size: 14.53 MB
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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com