clopen topology
21Cantor set — In mathematics, the Cantor set, introduced by German mathematician Georg Cantor in 1883 [Georg Cantor (1883) Über unendliche, lineare Punktmannigfaltigkeiten V [On infinite, linear point manifolds (sets)] , Mathematische Annalen , vol. 21, pages… …
22Dispersion point — In topology, a dispersion point or explosion point is a point in a topological space the removal of which leaves the space highly disconnected. More specifically, if X is a connected topological space containing the point p and at least two other …
23Equivalence of categories — In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are essentially the same . There are numerous examples of categorical equivalences… …
24Zero-dimensional space — In mathematics, a topological space is zero dimensional or 0 dimensional, if its topological dimension is zero, or equivalently, if it has a base consisting of clopen sets. A zero dimensional Hausdorff space is necessarily totally disconnected,… …
25Duality theory for distributive lattices — In mathematics, duality theory for distributive lattices provides three different (but closely related) representations of bounded distributive lattices via Priestley spaces, spectral spaces, and pairwise Stone spaces. This generalizes the well… …
26Cantor space — In mathematics, the term Cantor space is sometimes used to denotethe topological abstraction of the classical Cantor set:A topological space is aCantor space if it is homeomorphic to the Cantor set.The Cantor set itself is of course a Cantor… …
27Stone's representation theorem for Boolean algebras — In mathematics, Stone s representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of… …
28Empty set — ∅ redirects here. For similar looking symbols, see Ø (disambiguation). The empty set is the set containing no elements. In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality… …
29Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …
30Identity component — In mathematics, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group. Similarly, the identity path component of a topological group G is the path component of G that… …
