Topological Spaces: From Distance to Neighborhood - Brossura
Libro 7 di 168: Undergraduate Texts in Mathematics
Sinossi
Topological 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.
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Contenuti
I The Line And The Plane.- 1 What Topology Is About.- Topological Equivalence.- Continuity and Convergence.- A Few Conventions.- Extra: Topological Diversions.- Exercises.- 2 Axioms for ?.- Extra: Axiom Systems.- Exercises.- 3 Convergent Sequences and Continuity.- Subsequences.- Uniform Continuity.- The Plane.- Extra: Bolzano (1781-1848).- Exercises.- 4 Curves in the Plane.- Curves.- Homeomorphic Sets.- Brouwer’s Theorem.- Extra: L.E.J. Brouwer (1881-1966).- II Metric Spaces.- 5 Metrics.- Extra: Camille Jordan (1838-1922).- Exercises.- 6 Open and Closed Sets.- Subsets of a Metric Space.- Collections of Sets.- Similar Metrics.- Interior and Closure.- The Empty Set.- Extra: Cantor (1845-1918).- Exercises.- 7 Completeness.- Extra: Meager Sets and the Mazur Game.- Exercises.- 8 Uniform Convergence.- Extra: Spaces of Continuous Functions.- Exercises.- 9 Sequential Compactness.- Extra: The p-adic Numbers.- Exercises.- 10 Convergent Nets.- Inadequacy of Sequences.- Convergent Nets.- Extra: Knots.- Exercises.- 11 Transition to Topology.- Generalized Convergence.- Topologies.- Extra: The Emergence of the Professional Mathematician.- Exercises.- III Topological Spaces.- 12 Topological Spaces.- Extra: Map Coloring.- Exercises.- 13 Compactness and the Hausdorff Property.- Compact Spaces.- Hausdorff Spaces.- Extra: Hausdorff and the Measure Problem.- Exercises.- 14 Products and Quotients.- Product Spaces.- Quotient Spaces.- Extra: Surfaces.- Exercises.- 15 The Hahn-Tietze-Tong-Urysohn Theorems.- Urysohn’s Lemma.- Interpolation and Extension.- Extra: Nonstandard Mathematics.- Exercises.- 16 Connectedness.- Connected Spaces.- The Jordan Theorem.- Extra: Continuous Deformation of Curves.- Exercises.- 17 Tychonoff’s Theorem.- Extra: The Axiom of Choice.- Exercises.- IV Postscript.- 18 A Smorgasbord for Further Study.- Countability Conditions.- Separation Conditions.- Compactness Conditions.- Compactifications.- Connectivity Conditions.- Extra: Dates from the History of General Topology.- Exercises.- 19 Countable Sets.- Extra: The Continuum Hypothesis.- A Farewell to the Reader.- Literature.- Index of Symbols.- Index of Terms.
Product Description
Book by Buskes Gerard Rooij Arnoud van
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Topological Spaces (eng)
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Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics)
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Topological Spaces (Undergraduate Texts in Mathematics)
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Topological Spaces
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Springer New York Okt 2012, 2012
ISBN 10: 1461268621
ISBN 13: 9781461268628
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of 'Extras' at the end of each chapter presenting a brief foray outside topology. 332 pp. Englisch. Codice articolo 9781461268628
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Topological Spaces: From Distance to Neighborhood
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Springer-Verlag New York Inc., 2012
ISBN 10: 1461268621
ISBN 13: 9781461268628
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Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics)
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Paperback. Condizione: Brand New. reprint edition. 343 pages. 9.25x6.10x0.75 inches. In Stock. Codice articolo x-1461268621
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Topological Spaces
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move i. Codice articolo 4189499
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Topological Spaces
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Springer, Copernicus Okt 2012, 2012
ISBN 10: 1461268621
ISBN 13: 9781461268628
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 332 pp. Englisch. Codice articolo 9781461268628
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Topological Spaces : From Distance to Neighborhood
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Springer New York, Springer US, 2012
ISBN 10: 1461268621
ISBN 13: 9781461268628
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Taschenbuch
Da: AHA-BUCH GmbH, Einbeck, Germania
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9781461268628
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Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics)
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