n. pl. topolo·gies 1. Topographic study of a given place, especially the history of a region as indicated by its topography.
2. Medicine The anatomical structure of a specific area or part of the body.
3. Mathematics a. The study of certain properties that do not change as geometric figures or spaces undergo continuous deformation. These properties include openness, nearness, connectedness, and continuity.
b. The underlying structure that gives rise to such properties for a given figure or space: The topology of a doughnut and a picture frame are equivalent.
4. Computers The arrangement in which the nodes of a network are connected to each other.