In this thesis, we briefly present Brouwer fixed point theorem and the no retraction theorem. It turns out that the theorems are equivalent, which we also prove in this thesis. We present the basics of simplices and simplicial complexes. At the end of this thesis, we generalize the no retraction theorem to a broad class of compact 2-dimensional polyhedra. We conclude with an example that shows that the equivalence of the aforementioned theorems in general does not hold.
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