A spatial object consists of data assigned to points in a space. We develop an algebraic theory of spatial objects by modelling abstract data types of spatial objects as topological algebras of functions. One useful algebra is that of continuous functions, with operations lifted from operations on space and data, and equipped with the compactopen topology. We use terms as abstract syntax for dening spatial objects and conditional equational specications for reasoning. We pose a completeness problem: Given a selection of operations on spatial objects, do the terms approximate all the spatial objects to arbitrary accuracy? We give some general methods for solving the problem and consider their application to spatial objects with real number attributes.
['Kenneth Johnson', 'John V. Tucker']
The data type of spatial objects