(topology) A topology consisting of the empty set and all cofinite subsets of the underlying set.

(topology) A topology consisting only of the empty set and the underlying set.

plural of Alexandrov topology

(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.

(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.

(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.