Domain (a different concept)

[share]

According to Hans Hahn,[2]
the concept of a domain as an open connected set was introduced by
Constantin Carathéodory in his famous book (Carathéodory 1918).
Hahn also remarks that the word "Gebiet" ("Domain") was occasionally previously
used as a synonym of open set.[3]

However, the term "domain" was occasionally used to identify closely related
but slightly different concepts.
For example, in his influential monographs on elliptic partial differential equations,
Carlo Miranda uses the term "region" to identify an open connected set,[4][5]
and reserves the term "domain" to identify an internally connected,[6] perfect set,
each point of which is an accumulation point of interior points,[4]
following his former master Mauro Picone:[7] according to this convention,
if a set A is a region then its closure A is a domain.[4]

Wiki