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Enclaves and exclaves have special roles in geography and are of particular importance to fields such as (geo)politics and economy. However, enclaves and exclaves have not been defined with sufficient formality for automatic identification yet. To identify enclaves and exclaves more generally by computational means than current definitions existing in the literature, this article proposes expressive and generalized mathematical definitions of enclaves and exclaves based on point-set topology. A novel Boundary Extended 16-Intersection Model is developed in this article to identify enclaves, and 74 possible spatial configurations of enclaves are distinguished according to conditions of intersections for polygons in partitions and enclaves. The classic Dimensionally Extended 9-Intersection Model is employed to identify exclaves, and two possible spatial configurations of exclaves are distinguished according to conditions of intersections for polygons in partitions and exclaves. Applications of the proposed definitions are exemplified by the identification of enclaves and exclaves in prototypes and in the real world.

Identification of enclaves and exclaves by computation based on point-set topology