shape fibration, Fiber spaces in algebraic topology, shape equivalence, proper map between locally compact, separable metric ANR's, compacta in the Hilbert cube, shape theoretic properties of fiber fundamental sequences, FAR, complement theorems for fibrations, locally shape trivial, Compact (locally compact) metric spaces, Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties), fiber shape equivalences, Z-sets, fiber fundamental sequences, Generalizations of fiber spaces and bundles in algebraic topology, Shape theory, approximate fibrations