(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) Given a set X, a family of topological spaces (M_i,T_i)_(i∈I) and a family of functions f_i:X→M_i, the initial topology is the coarsest topology on X such that all f_i are continuous.

(topology) Given a set X, a family of topological spaces (M_i,T_i)_(i∈I) and a family of functions f_i:M_i→X, the final topology is the finest topology on X such that all f_i are continuous.

plural of relative topology

plural of subspace topology

plural of Zariski topology

plural of product topology

plural of discrete topology

plural of disjoint union topology

(topology) A topology which is applicable to the disjoint union of a given set of topological spaces and is the largest (most inclusive) topology that preserves the continuity of each contributing space as represented in the union.