Homotopy equivalence is a concept in topology that describes a relationship between two topological spaces. Two spaces, X and Y, are said to be homotopy equivalent if there exist continuous functions f: X → Y and g: Y → X such that the compositions g ∘ f and f ∘ g are homotopic to the identity maps on X and Y, respectively. This means that X can be continuously deformed into Y and vice versa. This relationship indicates that X and Y share the same topological properties, such as their fundamental groups and higher homotopy groups. Homotopy equivalence is a key concept in algebraic topology, allowing mathematicians to classify spaces based on their shape and structure rather than their specific details.