closed topology
31Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …
32Order topology — In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order …
33List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …
34Cocountable topology — The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose complement in X is countable. It follows that the only closed subsets are X and the… …
35Trivial topology — In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such a space is sometimes called an indiscrete space, and its topology sometimes called an indiscrete topology.… …
36Final topology — In general topology and related areas of mathematics, the final topology (inductive topology or strong topology) on a set X, with respect to a family of functions into X, is the finest topology on X which makes those functions continuous.… …
37Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …
38Triangulation (topology) — In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K , homeomorphic to X , together with a homeomorphism h : K o X . Triangulation is… …
39Chabauty topology — In mathematics, the Chabauty topology is a certain topological structure introduced in 1950 by Claude Chabauty, on the set of all closed subgroups of a locally compact group G. The intuitive idea may be seen in the case of the set of all lattices …
40Constructible set (topology) — For a Gödel constructive set, see constructible universe. In topology, a constructible set in a noetherian topological space is a finite union of locally closed sets. (A set is locally closed if it is the intersection of an open set and closed… …
