PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES

Abstract

For a map f : A ! X, there are concepts of H f spaces, T f -spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an H f -space, any H f -space is a T f space. For a principal fibration Ek ! X induced by k : X ! X ′ from ϵ : P X ′ ! X ′, we obtain some sufficient conditions to having liftings H (cid:22)f -structures and T (cid:22)f -structures on Ek of H f -structures and T f -structures on X respectively. We can also obtain some results about H f -spaces and T f -spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

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