By Sasho Kalajdzievski
An Illustrated creation to Topology and Homotopy explores the great thing about topology and homotopy conception in a right away and interesting demeanour whereas illustrating the facility of the idea via many, usually astonishing, functions. This self-contained ebook takes a visible and rigorous method that includes either large illustrations and entire 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 easy combinatorial workforce idea, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The final 3 chapters speak about the idea of protecting areas, the Borsuk-Ulam theorem, and functions in staff conception, together with numerous subgroup theorems.
Requiring just some familiarity with crew conception, the textual content contains a huge variety of figures in addition to quite a few examples that exhibit how the speculation may be utilized. every one part begins with short ancient notes that hint the expansion of the topic and ends with a collection of workouts.
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An Illustrated Introduction to Topology and Homotopy by Sasho Kalajdzievski
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