In this paper, we consider the exploration of topological environments 
by a robot with weak sensory capabilities. We assume only that the 
robot can recognize when it has reached a vertex, and can assign a 
cyclic ordering to the edges leaving a vertex with reference to the 
edge it arrived from. Given this limited sensing capability, and 
without the use of any markers or additional information, we will show 
that the construction of a topological map is still feasible. This is 
accomplished through both the exploration strategy which is designed to 
reveal model inconsistencies and by a search process that maintains a 
bounded set of believable world models throughout the exploration process.  
Plausible models are selected through the use of a ranking heuristic 
function based on the principle of Occam's Razor. We conclude with 
numerical simulations demonstrating the performance of the algorithm.