Abstract
In this part I we work in two categories namely the category of topological spaces and continuous maps, and the category of piecewise linear (PL) spaces and PL-maps. A PL-space is a topological space with a complete class of locally finite triangulations, any two of which have a common subdivision. A PL-mapf : X-~ Yis a continuous map between PL-spaces X and Y, which for some triangulation of X and Y maps every simplex of X linearly into a simplex of Y. We consider fibrebundles in the sense of STEENROD with a fixed crosssection, often called the zeroseetion,
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