cannot have gaps, state boundaries must coincide with county boundaries, counties must collectively cover states) that can be validated and corrected. Other systems, such as PostGIS, take a similar approach. 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. Topology in spatial analysis Several spatial analysis tools are ultimately based on the discovery of topological relationships between features: spatial query, in which one is searching for the features in one dataset based on desired topological relationships to the features of a second dataset. For example, "where are the student locations within the boundaries of School X?" spatial join, in which the attribute tables of two datasets are combined, with rows being matched based on a desired topological relationship between features in the two datasets, rather than using a stored key as in a normal table join in a relational database. For example, joining the attributes of a schools layer to the table of students based on which school boundary each student resides within. vector overlay, in which two layers (usually polygons) are merged, with new features being created where features from the two input datasets intersect. transport network analysis, a large class of tools in which connected lines (e.g., roads, utility infrastructure, streams) are analyzed using the mathematics of graph theory. The most common example is determining the optimal route between two locations through a street network, as implemented in most street web maps. Oracle and PostGIS provide fundamental topological operators allowing applications to test for "such relationships as contains, inside, covers, covered by, touch, and overlap with boundaries intersecting." Unlike the PostGIS documentation, the Oracle documentation draws a distinction between "topological relationships [which] remain constant when the coordinate space is deformed, such as by twisting or stretching" and "relationships that are not topological [which] include length of, distance between, and area of." These operators are leveraged by applications to ensure that data sets are stored and processed in a topologically correct fashion. However, topological operators are inherently complex and their implementation requires care to be taken with usability and conformance to standards. See also Digital topology Dimensionally Extended 9-Intersection Model References Geographic data and information Cartography Geometric topology Spatial analysis