Download PDF by Sasho Kalajdzievski: An Illustrated Introduction to Topology and Homotopy

By Sasho Kalajdzievski

ISBN-10: 1439848157

ISBN-13: 9781439848159

An Illustrated creation to Topology and Homotopy explores the wonderful thing about topology and homotopy thought in an instantaneous and interesting demeanour whereas illustrating the facility of the speculation via many, usually staggering, purposes. This self-contained booklet takes a visible and rigorous technique that includes either large illustrations and whole proofs.

The first a part of the textual content covers simple topology, starting from metric areas and the axioms of topology via subspaces, product areas, connectedness, compactness, and separation axioms to Urysohn’s lemma, Tietze’s theorems, and Stone-Čech compactification. targeting homotopy, the second one half starts off with the notions of ambient isotopy, homotopy, and the basic crew. The ebook then covers uncomplicated combinatorial team thought, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The final 3 chapters talk about the idea of masking areas, the Borsuk-Ulam theorem, and purposes in staff conception, together with a number of subgroup theorems.

Requiring just some familiarity with workforce concept, the textual content contains a huge variety of figures in addition to quite a few examples that convey how the idea may be utilized. every one part starts off with short old notes that hint the expansion of the topic and ends with a suite of routines.

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An Illustrated Introduction to Topology and Homotopy by Sasho Kalajdzievski

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