Sobriety in Terms of Nets

Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets. The usual criterion to check sobriety involves either irreducible closed subsets or completely prime lters of open sets. This paper provides an alternative possibility, thus trying to make sobriety easier to understand. We deene the notion of observative net, which, together with an appropriate convergence notion, characterizes sobriety.