By Sasho Kalajdzievski
An Illustrated advent to Topology and Homotopy explores the wonderful thing about topology and homotopy idea in an immediate and fascinating demeanour whereas illustrating the ability of the speculation via many, frequently mind-blowing, purposes. This self-contained booklet takes a visible and rigorous technique that includes either huge 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. concentrating on homotopy, the second one half starts off with the notions of ambient isotopy, homotopy, and the elemental workforce. The booklet then covers simple combinatorial workforce thought, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The final 3 chapters talk about the idea of protecting areas, the Borsuk-Ulam theorem, and purposes in workforce concept, together with numerous subgroup theorems.
Requiring just some familiarity with staff conception, the textual content encompasses a huge variety of figures in addition to quite a few examples that exhibit how the speculation should be utilized. every one part begins with short historic notes that hint the expansion of the topic and ends with a suite of routines.
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