This paper presents a mathematical technique for building perceptual models of urban areas. Concepts from point-set topology are used to develop a method of joining contiguous spatial units into relatively homogeneous clusters and to model how one homogeneous cluster blends or merges into the surrounding clusters. Both sharp and fuzzy borders between clusters are modeled. The technique is then used to model perceptual neighborhoods within a city and to explore how residential burglary rates vary between the interiors and borders of the neighborhoods.
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