The Conley index over a phase space for discrete semidynamical systems

We construct a discrete version of the Conley index over a base defined in [Mrozek et al., Trans. Amer. Math. Soc. 352 (2000) 4171] for flows. We also state and prove its properties. The index generalizes the homotopy Conley index defined in [Szymczak, Topology Appl. 66 (1995) 215].