n. a continuous deformation of one function or curve into another. A homotopy between a function and a constant is called null or inessential. The fundamental homotopy group at a point x of a topological space S, denoted Π₁(S, x), is composed of equivalence classes of closed paths through x, with juxtaposition of paths as multiplication. Higher homotopy groups are constructed analogously using generalized paths mapping hypercubes into the space. The fundamental homotopy groupoid of a topological space, S, denoted Π₁(S), is composed of equivalence classes of paths from x to y, with juxtaposition of paths as multiplication, where possible.