connected sites etc.

For locally connected toposes there is an easy condition on sites equivalent to connectedness. What about the general case? Moreover, I would be interested in a condition on sites equivalent to all maps from \Omega to \Delta(2) being constant. The reason for the question is quite specific. If one takes presheaves over the monoid Sp(2^N,2^N) of continuous endomaps of Cantor space 2^N it is straightforward to observe that \Pi(\Omega) \cong 1. I wonder whether this remains so when taking sheaves w.r.t. the topology generated by finite (disjoint) open covers. Thomas Streicher [For admin and other information see: http://www.mta.ca/~cat-dist/ ]