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Titlebook: Counterexamples in Topology; Lynn Arthur Steen,J. Arthur Seebach Book 1978Latest edition Springer-Verlag New York Inc. 1978 Compactificati

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書目名稱Counterexamples in Topology
編輯Lynn Arthur Steen,J. Arthur Seebach
視頻videohttp://file.papertrans.cn/240/239091/239091.mp4
圖書封面Titlebook: Counterexamples in Topology;  Lynn Arthur Steen,J. Arthur Seebach Book 1978Latest edition Springer-Verlag New York Inc. 1978 Compactificati
描述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
出版日期Book 1978Latest edition
關(guān)鍵詞Compactification; Connected space; Separation axiom; Topologie; metrizable; topology
版次2
doihttps://doi.org/10.1007/978-1-4612-6290-9
isbn_softcover978-0-387-90312-5
isbn_ebook978-1-4612-6290-9
copyrightSpringer-Verlag New York Inc. 1978
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Compactnessover. This difference between the separation axioms and the various forms of compactness is illustrated in the extreme by the double pointed finite complement topology (Example 18.7) which is not even T. yet does satisfy all the forms of compactness.
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Metric Spacess called a .. Although a single metric wall yield a unique topology on a given set, it is possible to find more than one metric which will yield the same topology. In fact, there are always an infinite number of metrics which will yield the same metric space (Example 134).
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Rainer Danielzyk,Ilse Helbrecht3 of Axiom 1 of [82] a Moore space. Each metric space is a Moore space, but not conversely, so the search for a metrization theorem became that of determining precisely which Moore spaces are metrizable. The most famous conjecture was that each normal Moore space is metrizable.
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Conjectures and Counterexamples3 of Axiom 1 of [82] a Moore space. Each metric space is a Moore space, but not conversely, so the search for a metrization theorem became that of determining precisely which Moore spaces are metrizable. The most famous conjecture was that each normal Moore space is metrizable.
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