👉 In mathematics, a homotopy is an equivalence relation on a topological space that captures the notion of "nearness" between points. It allows for the comparison of differentiable functions and provides a way to compare smooth manifolds. A fundamental example of a homotopy is the Hopf fibration, which is a universal covering map from the circle to the 3-sphere. The Hopf fibration is defined by two maps: 1. The first map is the constant map
