Abstract
A construction in a combinatorial geometry G is introduced, which generalizes truncations, and corresponds to the projection of an arbitrary set X on a given flat F of G. This projection is minimal among all weak maps which reduce the rank of F ∪ X to that of F. The hyperlane projections, i.e. when F is a hyperlane of G, form a lattice for the weak map order, and provide a characterization of the simple weak maps of G which preserve all independent sets of G except possible bases.
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