ETYM Greek topos place + -logy.
The branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence; SYN. analysis situs.

Study of places and their natural features; Mathematics, study or theory of the properties of a figure that is not affected by deformation; topographical study of one place; regional anatomy.
Branch of geometry that deals with those properties of a figure that remain unchanged even when the figure is transformed (bent, stretched)—for example, when a square painted on a rubber sheet is deformed by distorting the sheet.
Topology has scientific applications, as in the study of turbulence in flowing fluids.
The topological theory, proposed 1880, that only four colors are required in order to produce a map in which no two adjoining countries have the same color, inspired extensive research, and was proved 1972 by Kenneth Appel and Wolfgang Haken. The map of a subway system is an example of the topological representation of a network; connectivity (the way the lines join together) is preserved, but shape and size are not.

The configuration or layout of a network formed by the connections between devices on a LAN (local area network) or between two or more LANs. See also bus network, LAN, ring network, star network, token ring network, tree network.