Continuous change in spatial regions

When we survey the variety of kinds of spatial region, and the ways in which they can change over time, we find that the notion of continuity is not a simple all-or-nothing affair, and that spatial changes can vary in the manner and degree of continuity they exhibit. Little work appears to have been done on continuity in the context of spatial information theory, and this paper attempts to open up the field of investigation. Mathematics provides us with a paradigm case of continuity in the form of the standard ((E-S)) definition for continuous functions on the real numbers. We exploit this definition within the context of the great variety of types of spatial change by definining different measures of separation between regions, such that different changes may be continuous with respect to different selections from this set of measures. We apply these different forms of continuity in a discussion of various cases which can be regarded as idealisations of processes of change that are of interest in geography and other spatial sciences.