(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.

(graph theory, computer science) An ordering of the vertices of a directed graph such that if an edge goes from vertex u to vertex v then u precedes v in the ordering.

(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.

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

plural of topological vector space

(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.

(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.