Counterexamples in Topology - Softcover

Steen, L.A.

 
9780387903125: Counterexamples in Topology
Softcover
ISBN 10: 0387903127 ISBN 13: 9780387903125
Verlag: Springer, 2013

Inhaltsangabe

The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples. Al­ though it would be hazardous to claim that the creation of significant examples is less demanding than the development of theory, we have dis­ covered that focusing on examples is a particularly expeditious means of involving undergraduate mathematics students in actual research. Not only are examples more concrete than theorems-and thus more accessible-but they cut across individual theories and make it both appropriate and neces­ sary for the student to explore the entire literature in journals as well as texts. Indeed, much of the content of this book was first outlined by under­ graduate research teams working with the authors at Saint Olaf College during the summers of 1967 and 1968. In compiling and editing material for this book, both the authors and their undergraduate assistants realized a substantial increment in topologi­ cal insight as a direct result of chasing through details of each example. We hope our readers will have a similar experience. Each of the 143 examples in this book provides innumerable concrete illustrations of definitions, theo­ rems, and general methods of proof. There is no better way, for instance, to learn what the definition of metacompactness really means than to try to prove that Niemytzki’s tangent disc topology is not metacompact. The search for counterexamples is as lively and creative an activity as can be found in mathematics research.

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Reseña del editor

The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples. Al­ though it would be hazardous to claim that the creation of significant examples is less demanding than the development of theory, we have dis­ covered that focusing on examples is a particularly expeditious means of involving undergraduate mathematics students in actual research. Not only are examples more concrete than theorems-and thus more accessible-but they cut across individual theories and make it both appropriate and neces­ sary for the student to explore the entire literature in journals as well as texts. Indeed, much of the content of this book was first outlined by under­ graduate research teams working with the authors at Saint Olaf College during the summers of 1967 and 1968. In compiling and editing material for this book, both the authors and their undergraduate assistants realized a substantial increment in topologi­ cal insight as a direct result of chasing through details of each example. We hope our readers will have a similar experience. Each of the 143 examples in this book provides innumerable concrete illustrations of definitions, theo­ rems, and general methods of proof. There is no better way, for instance, to learn what the definition of metacompactness really means than to try to prove that Niemytzki's tangent disc topology is not metacompact. The search for counterexamples is as lively and creative an activity as can be found in mathematics research.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
0387903127
ISBN 13 
9780387903125
Einband
Tapa blanda
Auflage
2
Anzahl der Seiten
260
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Deutschland

Weitere beliebte Ausgaben desselben Titels

9780486687353: Counterexamples in Topology (Dover Books on MaTHEMA 1.4tics)

Vorgestellte Ausgabe

ISBN 10:  048668735X ISBN 13:  9780486687353
Verlag: Dover Publications Inc, 2003
Softcover