Giovanni Landi, Fedele Lizzi Projective Systems of Noncommutative Lattices as a Pregeometric Substratum (94K, LATeX 2e) ABSTRACT. We present an approximation to topological spaces by noncommutative lattices. This approximation has a deep physical flavour based on the impossibility to fully localize particles in any position measurement. The original space being approximated is recovered out of a projective limit.