The Maptree: A Fine-Grained Formal Representation of Space
This paper introduces a new formal structure, called the maptree, that is shown to uniquely specify, up to homeomorphism, the topological structure of embeddings of graphs in orientable, closed surfaces. A simple modification is made to show that the representation also works for planar embeddings. It is shown that the maptrees are capable of providing a rich representation of the topology of 2D spatial objects and their relationships. The maptree representation is then used to characterize some properties of topological change in these embeddings.
Keywordsmaptree topology topological change geographic information science theory
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