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In this paper we describe a model for navigation of an autonomous agent in which localization, path planning, and locomotion is performed in a qualitative manner instead of relying on exact coordinates. Our approach is grounded in a decomposition of navigable space based on a novel model of visibility and occlusion relations between extended objects for agents with very limited sensor abilities. A graph representation reflecting the adjacency between the regions of the decomposition is used as a topological map of the environment. The visibility-based representation can be constructed autonomously by the agent and navigation can be performed by simple reactive navigation behaviors. Moreover, the representation is well-qualified to be shared between multiple agents.