nLab domain (changes)

Showing changes from revision #11 to #12: Added | Removed | Changed

Disambiguation

There are multiple notions of domain of mathematics. These include:

• in ring theory:

  domain (ring theory) and integral domain

• in domain theory:

  Scott domains: pointed directed-complete partial orders

• in category theory:

  source of a morphism

• domain of discourse

• The subset $A\subseteq X$ for which there exists a relation $R\colon X \to Y$.

• in mathematical analysis , a a(n open) domain or region is a nonempty connected open subset of$\mathbb{R}^n$ (or $\mathbb{C}^n$, or topological manifold), see wikipedia: domain (mathematical_analysis) ) andeom: domain; a closure of an open domain is also called a closed domain

• in differential geometry and especially in complex analysis:

an open subset of a manifold (cf. Stein domain)