  We continue studying net bundles over partially ordered sets (posets),
defined as the analogues of ordinary fibre bundles. To this end, we analyze the
connection between homotopy, net homology and net cohomology of a poset, giving
versions of classical Hurewicz theorems. Focusing our attention on Hilbert net
bundles, we define the K-theory of a poset and introduce functions over the
homotopy groupoid satisfying the same formal properties as Chern classes. As
when the given poset is a base for the topology of a space, our results apply
to the category of locally constant bundles.
