n. 1. point set topology. the branch of mathematics that is concerned with the generalization of the concepts of continuity, limits, etc. to sets other than the real and complex numbers. 2. algebraic topology or (formerly) analysis situs. a branch of geometry describing the properties of a figure that are unaffected by continuous distortion such as stretching or knotting. See also knot. 3. a family of subsets of a given set that constitute a topological space. The discrete topology consists of the entire power set, while the indiscrete topology contains only the empty set and the entire space. The relative or induced topology on a subset is the topology constructed by taking intersections of the original topology with the subset. A topology, θ₁, is finer than another, θ₂, if θ₁ is a refinement of θ₂, and θ₂ is then said to be coarser than θ₁. Thus on any given set, the discrete topology is the finest topology and the indiscrete topology is the coarsest.