Topology: 2nd edition

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urn:lcp:topology0002edmunk:epub:078f159a-239e-4b16-ad86-ee268f263c30 Foldoutcount 0 Identifier topology0002edmunk Identifier-ark ark:/13960/s2zj69n2956 Invoice 1652 Isbn 8120320468

James Munkres - Wikipedia

Advanced topics—Such as metrization and imbedding theorems, function spaces, and dimension theory are covered after connectedness and compactness. NEW - Greatly expanded, full-semester coverage of algebraic topology—Extensive treatment of the fundamental group and covering spaces. What follows is a wealth of applications—to the topology of the plane (including the Jordan curve theorem), to the classification of compact surfaces, and to the classification of covering spaces. A final chapter provides an application to group theory itself. I'm currently studying Algebraic Topology and Differential Topology (and Differential Geometry) on my own, and I'm thoroughly enjoying it, but currently it seems that Algebraic Topology and Differential Topology, don't use that much General Topology apart from Compactness, Connectedness and the basics. I've yet to see (in my limited knowledge of Alg and Diff Topology) any real use of things like Separation Axioms and deeper theory from General Topology. Carefully guides students through transitions to more advanced topics being careful not to overwhelm them. Motivates students to continue into more challenging areas. Ex.___ Access-restricted-item true Addeddate 2022-01-25 17:07:37 Autocrop_version 0.0.5_books-20210916-0.1 Bookplateleaf 0008 Boxid IA40327619 Camera Sony Alpha-A6300 (Control) Collection_set printdisabled External-identifierFollows the present-day trend in the teaching of topology which explores the subject much more extensively with one semester devoted to general topology and a second to algebraic topology. Ex.___ Greatly expanded, full-semester coverage of algebraic topology—Extensive treatment of the fundamental group and covering spaces. What follows is a wealth of applications—to the topology of the plane (including the Jordan curve theorem), to the classification of compact surfaces, and to the classification of covering spaces. A final chapter provides an application to group theory itself. Munkres, James R. (2000). Topology (Seconded.). Upper Saddle River, NJ: Prentice Hall, Inc. ISBN 978-0-13-181629-9. OCLC 42683260. There are other subfields of topology. One subfield is algebraic topology, which uses algebraic tools to rigorously express intuitions such as “holes.” For example, how is a hollow sphere different from a hollow torus? One may say that the torus has a “hole” in it while the sphere does not. This intuition is captured by the notion of the fundamental group, which, (very) loosely speaking, is an algebraic object that counts the number of “holes” of a topological space. There are other useful algebraic tools, including various homology and cohomology theories. These can all be viewed as a mapping from the category of topological spaces to algebraic objects, and are very good examples of functors in the language of category theory; it is for this reason that many algebraic topologists are also interested in category theory. He was elected to the 2018 class of fellows of the American Mathematical Society. [5] Textbooks [ edit ]

Topology, Pearson New International Edition

Deepen students' understanding of concepts and theorems just presented rather than simply test comprehension. The supplementary exercises can be used by students as a foundation for an independent research project or paper. Ex.___ Below are links to answers and solutions for exercises in the Munkres (2000) Topology, Second Edition. Topology, in broad terms, is the study of those qualities of an object that are invariant under certain deformations. Such deformations include stretching but not tearing or gluing; in laymen’s terms, one is allowed to play with a sheet of paper without poking holes in it or joining two separate parts together. (A popular joke is that for topologists, a doughnut and a coffee mug are the same thing, because one can be continuously transformed into the other.) One-or two-semester coverage—Provides separate, distinct sections on general topology and algebraic topology. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences. FeaturesIf I want to broaden my knowledge of General Topology, what book do I go to next after Munkres? Should I learn some Pointfree Topology (Frame Theory)?. Also I should mention that I don't want to specialize in General Topology.