(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.

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

(functional analysis) A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions.