Topology: 2nd edition

Product Information

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.

Topology; A First Course: Munkres, James: 9780139254956 Topology; A First Course: Munkres, James: 9780139254956

Ocr tesseract 5.0.0-1-g862e Ocr_detected_lang en Ocr_detected_lang_conf 1.0000 Ocr_detected_script Latin Ocr_detected_script_conf 0.9936 Ocr_module_version 0.0.14 Ocr_parameters -l eng Old_pallet IA-WL-0000203 Openlibrary_editionMunkres completed his undergraduate education at Nebraska Wesleyan University [2] and received his Ph.D. from the University of Michigan in 1956; his advisor was Edwin E. Moise. Earlier in his career he taught at the University of Michigan and at Princeton University. [2] A topology on an object is a structure that determines which subsets of the object are open sets; such a structure is what gives the object properties such as compactness, connectedness, or even convergence of sequences. For example, when we say that [0,1] is compact, what we really mean is that with the usual topology on the real line R, the subset [0,1] is compact. We could easily give R a different topology (e.g., the lower limit topology), such that the subset [0,1] is no longer compact. Point-set topology is the subfield of topology that is concerned with constructing topologies on objects and developing useful notions such as separability and countability; it is closely related to set theory. If 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. Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math., vol. 72 (1960)

Munkres - Academia.edu Topologia 2ed R. Munkres - Academia.edu

For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. 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.) While I certainly have a lot more Differential Topology and Algebraic Topology to learn (and I look forward to it), I also feel like I should learn a bit more of General Topology.Notes on the adjunction, compactification, and mapping space topologies from John Terilla's topology course. This book provides 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 After making my way through Dover's excellent Algebraic Topology and Combinatorial Topology (sadly out of print), I was recommended this on account of its 'clean, accessible' (1) layout, and its wise choice of 'not completely dedicating itself to the Jordan (curve) theorem'. (2) Carefully guides students through transitions to more advanced topics being careful not to overwhelm them. Motivates students to continue into more challenging areas. Ex.___ 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.

Topology - MIT Mathematics Intro to Topology - MIT Mathematics

I found it to be an even better approach to the subject than the Dover books. That said, they're all highly recommended. However, one new(er) to the concepts of algebraic and general topology will probably find this book to be more accessible, even if the algebraic treatment is too light to properly slake the gullet of a more seasoned topologist. Among Munkres' contributions to mathematics is the development of what is sometimes called the Munkres assignment algorithm. A significant contribution in topology is his obstruction theory for the smoothing of homeomorphisms. [3] [4] These developments establish a connection between the John Milnor groups of differentiable structures on spheres and the smoothing methods of classical analysis. He was elected to the 2018 class of fellows of the American Mathematical Society. [5] Textbooks [ edit ] 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-identifier 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. FeaturesGitHub repository here, HTML versions here, and PDF version here. Contents Chapter 1. Set Theory and Logic Extend your professional development and meet your students where they are with free weekly Digital Learning NOW webinars. Attend live, watch on-demand, or listen at your leisure to expand your teaching strategies. Earn digital professional development badges for attending a live session. The study of 1- and 2-manifolds is arguably complete – as an exercise, you can probably easily list all 1-manifolds without much prior knowledge, and inexplicably, much about manifolds of dimension greater than 4 is known. However, for a long time, many aspects of 3- and 4-manifolds had evaded study; thus developed the subfield of low-dimensional topology, the study of manifolds of dimension 4 or below. This is an active area of research, and in recent years has been found to be closely related to quantum field theory in physics. Unless one is (and you are not!) planning to write a PhD thesis in General Topology, Munkres is (more than) enough.