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The book presents the theory of topological degree as a tool for stably counting the solutions of nonlinear equations while taking orientation into account.It first develops the Brouwer degree in finite dimensions, establishes its properties (axioms, homotopy invariance, stability), and uses it to prove topological results such as Brouwer's fixed point theorem and the non-retractability of the sphere.The theory is then extended to the infinite-dimensional setting through the Leray-Schauder degree for compact operators, leading to general fixed point theorems and existence results for boundary value problems in ordinary and partial differential equations.
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