Illustrated Introduction To Topology And Homotopy
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Author | : Sasho Kalajdzievski |
Publisher | : CRC Press |
Total Pages | : 488 |
Release | : 2015-03-24 |
Genre | : Mathematics |
ISBN | : 1482220814 |
An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs
Author | : SASHO. KALAJDZIEVSKI |
Publisher | : |
Total Pages | : |
Release | : 2023 |
Genre | : |
ISBN | : 9781138583412 |
Author | : Sasho Kalajdzievski |
Publisher | : CRC Press |
Total Pages | : 152 |
Release | : 2020-08-13 |
Genre | : Mathematics |
ISBN | : 1000158160 |
This solution manual accompanies the first part of the book An Illustrated Introduction toTopology and Homotopy by the same author. Except for a small number of exercises inthe first few sections, we provide solutions of the (228) odd-numbered problemsappearing in first part of the book (Topology). The primary targets of this manual are thestudents of topology. This set is not disjoint from the set of instructors of topologycourses, who may also find this manual useful as a source of examples, exam problems,etc.
Author | : Taylor & Francis Group |
Publisher | : |
Total Pages | : |
Release | : 2012-05-15 |
Genre | : |
ISBN | : 9781439848203 |
An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn s lemma, Tietze s theorems, and Stone- ech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems. Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts with brief historical notes that trace the growth of the subject and ends with a set of exercises. "
Author | : Allan J. Sieradski |
Publisher | : Brooks/Cole |
Total Pages | : 510 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : |
This text is an introduction to topology and homotopy. Topics are integrated into a coherent whole and developed slowly so students will not be overwhelmed.
Author | : Sasho Kalajdzievski |
Publisher | : CRC Press |
Total Pages | : 110 |
Release | : 2020-08-13 |
Genre | : Mathematics |
ISBN | : 1000115364 |
This solution manual accompanies the first part of the book An Illustrated Introduction toTopology and Homotopy by the same author. Except for a small number of exercises inthe first few sections, we provide solutions of the (228) odd-numbered problemsappearing in first part of the book (Topology). The primary targets of this manual are thestudents of topology. This set is not disjoint from the set of instructors of topologycourses, who may also find this manual useful as a source of examples, exam problems,etc.
Author | : Martin Arkowitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2011-07-25 |
Genre | : Mathematics |
ISBN | : 144197329X |
This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.
Author | : V. A. Vasilʹev |
Publisher | : American Mathematical Soc. |
Total Pages | : 165 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821821628 |
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."
Author | : Michael Henle |
Publisher | : Courier Corporation |
Total Pages | : 340 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780486679662 |
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Author | : Theodore W. Gamelin |
Publisher | : Courier Corporation |
Total Pages | : 258 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 0486320189 |
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.