Homotopy equivalence is a relationship between two topological spaces that indicates they can be transformed into one another through continuous deformations, known as homotopies. This concept implies that the two spaces share the same topological properties and allows one to transfer information between them, particularly in the study of homology and cohomology, where it helps establish isomorphisms of their respective algebraic structures. Additionally, homotopy equivalence serves as a crucial foundation for understanding more complex relationships in homological algebra and the application of the Eilenberg-Steenrod axioms.
congrats on reading the definition of homotopy equivalence. now let's actually learn it.