Rarely are maps topologically clean when digitized or imported. A GIS has to be able to build topology from unconnected arcs. Nodes that are close together are snapped. Slivers due to double digitizing and overlay are eliminated. The tolerances controlling snapping, elimination, and merging must be considered carefully, because they can move features.
Complete topology makes map overlay feasible.
Topology allows many GIS operations to be done without accessing the point files. TINs use an optimal Delaunay triangulation of a set of irregularly distributed points. TINs are popular in CAD and surveying packages. Triangulated Irregular Network Way to handle field data with the vector data structure. More efficient than a grid.