General Topology I

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General Topology I

Author : A.V. Arkhangel'skii
Publisher : Springer Science & Business Media
ISBN 13 : 3642612652
Total Pages : 210 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis General Topology I by : A.V. Arkhangel'skii

Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.

General Topology I

Author : A.V. Arkhangel'skii
Publisher : Springer
ISBN 13 : 9783642612664
Total Pages : 202 pages
Book Rating : 4.6/5 (126 download)

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Book Synopsis General Topology I by : A.V. Arkhangel'skii

Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer. This book was released on 2011-11-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

General Topology I

Author : A.V. Arkhangel'skii
Publisher : Springer
ISBN 13 : 9783642647673
Total Pages : 0 pages
Book Rating : 4.6/5 (476 download)

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Book Synopsis General Topology I by : A.V. Arkhangel'skii

Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer. This book was released on 2011-09-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a topological space and a continuous map, were introduced by Hausdorffin 1914. Oneofthecentralproblemsoftopologyisthedeterminationandinvestigation of topological invariants; that is, properties ofspaces which are preserved under homeomorphisms. Topological invariants need not be numbers. Connectedness, compactness, andmetrizability, forexample, arenon-numericaltopologicalinvariants.Dimen- sional invariants, on the otherhand, areexamplesofnumericalinvariants which take integervalues on specific topological spaces. Part II ofthis book is devoted to them. Topological invariants which take values in the cardinal numbers play an especially important role, providing the raw material for many useful coin" putations. Weight, density, character, and Suslin number are invariants ofthis type. Certain classes of topological spaces are defined in terms of topological in- variants. Particularly important examples include the metrizable spaces, spaces with a countable base, compact spaces, Tikhonov spaces, Polish spaces, Cech- complete spaces and the symmetrizable spaces.

General Topology

Author : John L. Kelley
Publisher : Courier Dover Publications
ISBN 13 : 0486820661
Total Pages : 321 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis General Topology by : John L. Kelley

Download or read book General Topology written by John L. Kelley and published by Courier Dover Publications. This book was released on 2017-03-07 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.

Encyclopedia of General Topology

Author : K.P. Hart
Publisher : Elsevier
ISBN 13 : 0080530869
Total Pages : 537 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Encyclopedia of General Topology by : K.P. Hart

Download or read book Encyclopedia of General Topology written by K.P. Hart and published by Elsevier. This book was released on 2003-11-18 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms

General Topology

Author : Waclaw Sierpinski
Publisher : Courier Dover Publications
ISBN 13 : 0486842541
Total Pages : 305 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis General Topology by : Waclaw Sierpinski

Download or read book General Topology written by Waclaw Sierpinski and published by Courier Dover Publications. This book was released on 2020-04-15 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critically acclaimed text by distinguished mathematician presents detailed theory of Fréchet (V) spaces and comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. 1956 edition.

General Topology

Author : Tom Richmond
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110686724
Total Pages : 397 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis General Topology by : Tom Richmond

Download or read book General Topology written by Tom Richmond and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.

General Topology

Author : J. Dixmier
Publisher : Springer Science & Business Media
ISBN 13 : 1475740328
Total Pages : 150 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis General Topology by : J. Dixmier

Download or read book General Topology written by J. Dixmier and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoing alone does not justify the very general framework in which this course is set. The fact is that the concepts mentioned above have shown themselves to be useful for objects other than the real numbers.

The General Topology of Dynamical Systems

Author : Ethan Akin
Publisher : American Mathematical Soc.
ISBN 13 : 0821849328
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The General Topology of Dynamical Systems by : Ethan Akin

Download or read book The General Topology of Dynamical Systems written by Ethan Akin and published by American Mathematical Soc.. This book was released on 1993 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.

General Topology

Author : Stephen Willard
Publisher : Courier Corporation
ISBN 13 : 0486131785
Total Pages : 386 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis General Topology by : Stephen Willard

Download or read book General Topology written by Stephen Willard and published by Courier Corporation. This book was released on 2012-07-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Modern General Topology

Author : Jun-Iti Nagata
Publisher : Elsevier
ISBN 13 : 1483278166
Total Pages : 376 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Modern General Topology by : Jun-Iti Nagata

Download or read book Modern General Topology written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.

Foundations of General Topology

Author : William J. Pervin
Publisher : Academic Press
ISBN 13 : 1483225151
Total Pages : 222 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Foundations of General Topology by : William J. Pervin

Download or read book Foundations of General Topology written by William J. Pervin and published by Academic Press. This book was released on 2014-05-12 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.

Geometric Aspects of General Topology

Author : Katsuro Sakai
Publisher : Springer Science & Business Media
ISBN 13 : 443154397X
Total Pages : 539 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Geometric Aspects of General Topology by : Katsuro Sakai

Download or read book Geometric Aspects of General Topology written by Katsuro Sakai and published by Springer Science & Business Media. This book was released on 2013-07-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.

Cape Cod

Author : Henry David Thoreau
Publisher :
ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.:/5 (32 download)

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Book Synopsis Cape Cod by : Henry David Thoreau

Download or read book Cape Cod written by Henry David Thoreau and published by . This book was released on 1892 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to General Topology

Author : K. D. Joshi
Publisher : New Age International
ISBN 13 : 9780852264447
Total Pages : 430 pages
Book Rating : 4.2/5 (644 download)

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Book Synopsis Introduction to General Topology by : K. D. Joshi

Download or read book Introduction to General Topology written by K. D. Joshi and published by New Age International. This book was released on 1983 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topology I

Author : S.P. Novikov
Publisher : Springer Science & Business Media
ISBN 13 : 3662105799
Total Pages : 326 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Topology I by : S.P. Novikov

Download or read book Topology I written by S.P. Novikov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.

General Topology and Homotopy Theory

Author : I.M. James
Publisher : Springer Science & Business Media
ISBN 13 : 1461382831
Total Pages : 253 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis General Topology and Homotopy Theory by : I.M. James

Download or read book General Topology and Homotopy Theory written by I.M. James and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.