(mathematics) A field that is also a topological space in which addition and multiplication are both continuous.

plural of topological field

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

(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.