Fundamental dimension and suspension of approximate fibrations

Abstract

Given an approximate fibration f : X → Y f:X \to Y between ANR’s a new approximate fibration Sf is constructed with the property that the fibers of Sf are the suspensions of the fibers of f. This construction is used together with an approximation theorem of T. Chapman to give conditions under which Fd X = Fd Y + Fd f − 1 ( x ) {\text {Fd}}\;X = {\text {Fd}}\;Y + {\text {Fd}}\;{f^{ - 1}}(x) .