Assignment:
We prove a generalization of Brouwer’s Fixed Point Theorem to compact sets that are not necessarily convex, but are homeomorphic to a convex set. Two compact sets X and Y in Rn are called homeomorphic if there exists a continuous bijection g : X → Y satisfying the property that g−1 is also continuous.8 Prove that if X ⊆ Rn is a compact set that is homeomorphic to a convex and compact set Y and if f : X → X is a continuous function, then f has a fixed point.
Provide complete and step by step solution for the question and show calculations and use formulas.