(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.

(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.

The general field of topology, not restricting attention to specific classes of spaces, and not using algebraic topology.

plural of topological space

plural of topological group

(topology) A group which is also a topological space and whose group operations are continuous functions.

(topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);

plural of topological insulator