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Product Identifiers
PublisherSpringer New York
ISBN-100387949941
ISBN-139780387949949
eBay Product ID (ePID)1122196
Product Key Features
Number of PagesXi, 313 Pages
LanguageEnglish
Publication NameTopological Spaces : from Distance to Neighborhood
Publication Year1997
SubjectTopology
TypeTextbook
Subject AreaMathematics
AuthorArnoud Van Rooij, Gerard Buskes
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight50.1 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN97-003756
Dewey Edition21
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal514/.322
Table Of ContentI The Line And The Plane.- 1 What Topology Is About.- 2 Axioms for ?.- 3 Convergent Sequences and Continuity.- 4 Curves in the Plane.- II Metric Spaces.- 5 Metrics.- 6 Open and Closed Sets.- 7 Completeness.- 8 Uniform Convergence.- 9 Sequential Compactness.- 10 Convergent Nets.- 11 Transition to Topology.- III Topological Spaces.- 12 Topological Spaces.- 13 Compactness and the Hausdorff Property.- 14 Products and Quotients.- 15 The Hahn-Tietze-Tong-Urysohn Theorems.- 16 Connectedness.- IV Postscript.- 18 A Smorgasbord for Further Study.- 19 Countable Sets.- Literature.- Index of Symbols.- Index of Terms.
SynopsisTopological Spaces: From Distance to Neighborhood is a gentle introduction to topological spaces leading the reader to understand the notion of what is important in topology vis-a-vis geometry. The authors have carefully divided the book into three sections; The line and the plane, Metric spaces and Topological spaces, in order to mitigate the the move into higher levels of abstraction. Students will be very attracted to this presentation., This book is a text, not a reference, on Point-set Thpology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. Th most beginners, Thpology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. Th mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Thpological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Thpology preeminently is a subject with an extensive ar ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. Th meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric., This book is a text, not a reference, on Point-set Thpology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. Th most beginners, Thpology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. Th mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Thpological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Thpology preeminently is a subject with an extensive ar- ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. Th meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com- plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric., This book is a text, not a reference, on Point-set Topology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. To most beginners, Topology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. To mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Topological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Topology preeminently is a subject with an extensive array of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. To meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, complete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric.
LC Classification NumberQA611-614.97
