Geospatial topology

It is thus the application of the mathematics of topology to GIS, and is distinct from, but complementary to the many aspects of geographic information that are based on quantitative spatial measurements through coordinate geometry.

One of the first developments of Geographic Information Science in the early 1990s was the work of Max Egenhofer, Eliseo Clementini, Peter di Felice, and others to develop a concise theory of such relations commonly called the 9-Intersection Model, which characterizes the range of topological relationships based on the relationships between the interiors, exteriors, and boundaries of features.

By the 1990s, the combination of cheaper storage and new users who were not concerned with topology led to a resurgence in spaghetti data structures, such as the shapefile.

A very different approach is to not store topological information in the data at all, but to construct it dynamically, usually during the editing process, to highlight and correct possible errors; this is a feature of GIS software such as ArcGIS Pro and QGIS.

These operators are leveraged by applications to ensure that data sets are stored and processed in a topologically correct fashion.