By Sasho Kalajdzievski
An Illustrated creation to Topology and Homotopy explores the wonderful thing about topology and homotopy idea in an immediate and interesting demeanour whereas illustrating the facility of the speculation via many, frequently spectacular, functions. This self-contained publication takes a visible and rigorous process that includes either vast illustrations and entire proofs.
The first a part of the textual content covers uncomplicated 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 begins with the notions of ambient isotopy, homotopy, and the basic crew. The publication then covers simple combinatorial crew thought, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The final 3 chapters speak about the idea of overlaying areas, the Borsuk-Ulam theorem, and functions in team conception, together with a number of subgroup theorems.
Requiring just some familiarity with workforce conception, the textual content encompasses a huge variety of figures in addition to quite a few examples that convey how the speculation should be utilized. every one part starts off with short ancient notes that hint the expansion of the topic and ends with a suite of routines.
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Extra info for An Illustrated Introduction to Topology and Homotopy
An Illustrated Introduction to Topology and Homotopy by Sasho Kalajdzievski