Area (mathematics)

In topology and analysis , the term area describes an open , non-empty and coherent subset of a topological space . In many theorems of function theory it is assumed that the functions under consideration are defined in one area and are holomorphic or meromorphic there.

Comments and examples

• ${\displaystyle D\subset \mathbb {C} }$is called star region if D is star-shaped and a region.
• ${\displaystyle D\subset \mathbb {C} }$is called convex region if D is convex and a region.
• Every convex region is a star region.

See also

• Complex numbers
• Plain area
• Star region

literature

• Kurt Endl, Wolfgang Luh : Analysis. Volume 2. 7th revised edition. Aula-Verlag, Wiesbaden 1989, ISBN 3-89104-455-0 , p. 224.

Web links

Wiktionary: Territory  - explanations of meanings, word origins, synonyms, translations

• Area in curve integrals and conservative vector fields on Mathematik Online (Uni Stuttgart)