2013
DOI: 10.1142/9789814425926_0007
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Abstract: This thesis will thoroughly examine the basic ideas of homotopy theory and follow this with a treatment of the fundamental group and several other important results. The goal of this thesis is to use these ideas and show my understanding of them to prove the fundamental theorem of algebra and the Brouwer fixed-point theorem for the disc. always exists for f, f : X → Y when Y is a convex set, which is a subset of a vector space such that ∀a, b ∈ Y and ∀t ∈ [0, 1], ta + (1 − b)t ∈ Y. Moreover, two maps into a co…

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