(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.

plural of Zariski topology

(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.

plural of Alexandrov topology

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

plural of pointless topology

(mathematics) An approach to topology that avoids mentioning points.

(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.

(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.