(Internet) The study of the linked structure of the World Wide Web.

(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.

(topology) subspace topology

(topology) The topology of a subset S of a topological space X which is obtained by considering any subset of S to be an open set if it corresponds to the intersection of S with some open set of X.

(topology) The topology of the real number system generated by a basis which consists of all open balls (in the real number system), which are defined in terms of the one-dimensional Euclidean metric.

(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper.

(category theory) A structure on a category which makes the category's objects act like the open sets of a topological space.

(topology) A topology consisting of the empty set and all cofinite subsets of the underlying set.

(topology) A topology consisting only of the empty set and the underlying set.

(topology) A topology in which the intersection of any family of open sets is an open set.