Gf -SPACES FOR MAPS AND POSTNIKOV SYSTEMS
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Abstract
For a map f : A → X, we define and study a concept of Gf -space for a map, which is a generalized one of a G-space. Any G-space is a Gf -space, but the converse does not hold. In fact, S2 is a Gη-space, but not G-space. We show that X is a Gf -space if and only if Gn(A, f, X) = πn(X) for all n. It is clear that any H f -space is a Gf -space and any Gf -space is a W f -space. We can also obtain some results about Gf -spaces in Postnikov systems for spaces, which are generalization of Haslam's results about G-spaces.
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