  We investigate the exploration of networks by a mobile agent. It is long
known that, without global information about the graph, it is not possible to
make the agent halts after the exploration except if the graph is a tree. We
therefore endow the agent with binoculars, a sensing device that can show the
local structure of the environment at a constant distance of the agent current
location. We show that, with binoculars, it is possible to explore and halt in
a large class of non-tree networks. We give a complete characterization of the
class of networks that can be explored using binoculars using standard notions
of discrete topology. Our characterization is constructive, we present an
Exploration algorithm that is universal; this algorithm explores any network
explorable with binoculars, and never halts in non-explorable networks.
