Algebraic Topology Invariants

Two continuous functions f,g: X → Y from a topological space X to another, Y are called homotopic if one can be "continuously deformed " into the other. Such a deformation is called a homotopy H: X × I → Y between the two functions. Two spaces X,Y are called homotopy equivalent if there are continous maps f: X → Y and g: Y → X that are homotopy inverse to each other, i.e., such that g ◦ f ' idX and f ◦ g ' idY. Martin Raussen Directed algebraic topology and application