{"product_id":"counterexamples-in-topology-9780387903125","title":"Counterexamples in Topology","description":"\u003cp\u003eThe 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 Niemytzkis tangent disc topology is not metacompact. The search for counterexamples is as lively and creative an activity as can be found in mathematics research.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45651435388981,"sku":"ByrdShop_0387903127","price":95.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780387903125.jpg?v=1781834665","url":"https:\/\/atxbooks.com\/products\/counterexamples-in-topology-9780387903125","provider":"ATX Books","version":"1.0","type":"link"}