topology
The spatial relationships between connecting or adjacent coverage features (e.g., arcs,
nodes, polygons, and points). For example, the topology of an arc includes its from- and
to-nodes, and its left and right polygons. Topological relationships are built from simple
elements into complex elements: points (simplest elements), arcs (sets of connected
points), areas (sets of connected arcs), and routes (sets of sections, which are arcs or
portions of arcs). Redundant data (coordinates) are eliminated because an arc may
represent a linear feature, part of the boundary of an area feature, or both. Topology is
useful in GIS because many spatial modeling operations don’t require coordinates,
only topological information. For example, to find an optimal path between two points
requires a list of the arcs that connect to each other and the cost to traverse each arc
in each direction. Coordinates are only needed for drawing the path after it is
calculated.
(from ARC/INFO 7.1 help)
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