Vol. 15, No. 4, 1965

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On the continuous image of a singular chain complex

Glen Eugene Bredon

Vol. 15 (1965), No. 4, 1115–1118

A continuous surjection π : X Y between topological spaces is called “ductile” if, for each y Y and neighborhood U of y there is a neighborhood V of y which contracts to y through U in such a way that this contraction can be covered by a homotopy of π1(V ). It is shown, in this note, that if π : X Y is ductile and Y is paracompact then the inclusion of the image πC(X) of the singular chain complex of X in the singular chain complex C(Y ) of Y induces an isomorphism in homology. Thus H(Y ) can be computed from those singular simplices of Y which are images of singular simplices of X.

Mathematical Subject Classification
Primary: 55.30
Received: 22 September 1964
Published: 1 December 1965
Glen Eugene Bredon