Two Term Conditions in π Exact Couples

Abstract

In achieving his celebrated results on the homology groups of fibre spaces, J. P. Serre used the exact couple of a fibring defined by J. Leray. One of his main tools was the so-called two-term condition on the E2 term of this exact couple, which, if satisfied, yielded exact sequences, such as those of Gysin and Wang (see (5), Chapter IX). H. Fédérer, in (3), defined an exact couple (X, F, v) on the mapping space M(X, Y) = {ƒ:X → Y|X, Y are spaces and ƒ is continuous} with the compact-open topology, where X is a locally finite CW complex and Y is arc-connected and n-simple for all n.