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Sto caricando le informazioni... Counterexamples in Topologydi Lynn Arthur Steen, J. Arthur Seebach, Jr.
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Iscriviti per consentire a LibraryThing di scoprire se ti piacerà questo libro. Attualmente non vi sono conversazioni su questo libro. Every student of topology should have this. Steen and Seebach provide instances to illustrate every distinction commonly made in topology (e.g. regular but not normal, T1 but not Hausdorff). In the latter part of the book the authors offer a thorough discussion of metrizability (under what conditions can a topological space be given a metric that "agrees" with its topology?). This book contains a dense covering of point-set topology and over a hundred different topologies over different spaces (as per the book count; some of those include more than one topology over the same space, or one topology over several spaces.) You can learn a great deal about topology just from this book without help. While there are no exercises and no proofs, there are plenty of examples to show why one property of a topology is or is not dependent on another. Thinking your way through the introduction and examples is a great way to learn. On the down side, there's a topology paper included as an appendix that has little to do with the book and seems to be included just as an important paper on topology. It's way above my head, and I suspect it will be for many years. Also, the exercises seem randomly ordered, which is less of a problem because they are heavily linked by number from all over the book. nessuna recensione | aggiungi una recensione
Appartiene alle Collane Editoriali
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. Non sono state trovate descrizioni di biblioteche |
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Google Books — Sto caricando le informazioni... GeneriSistema Decimale Melvil (DDC)514.3Natural sciences and mathematics Mathematics Topology Topology of SpaceClassificazione LCVotoMedia:
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