Topology is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these properties are the topological invariants. On its own, topology defines a "rubber" model, whose position is not fixed in space. For example, a circular edge and an elliptical edge are topologically equivalent, but not geometrically. Likewise, a square face and a trapezoidal face are topologically equivalent, but not geometrically. A topological entity's shape, position, and orientation are fixed in space when it is associated with a geometric entity. In ACIS, the topology describes the adjacency and connectivity relationships between the various objects in the ACIS model. This is the basis of a Boundary Representation, or B-rep, model.
ACIS separately represents the topology (connectivity) and the geometry (detailed shape) of objects. This "boundary representation" model structure allows you to determine whether a position is inside, outside, or on the boundary of a volume. (This distinguishes a solid modeler from a surface or wireframe modeler.) The "boundary" in "boundary representation" is the boundary between solid material and empty space. This boundary is made from a closed set of surfaces.
ACIS topology can be bounded, unbounded, or semi-bounded, allowing for complete and incomplete bodies. A solid, for example, can have missing faces, and existing faces can have missing edges. Solids can have internal faces that divide the solid into cells. Bodies such as these are not physically realizable, but can be represented with ACIS.