Historical notes Domain (mathematical analysis)

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according hans hahn, concept of domain open connected set introduced constantin carathéodory in famous book (carathéodory 1918). hahn remarks word gebiet ( domain ) used synonym of open set.


however, term domain used identify closely related different concepts. example, in influential monographs on elliptic partial differential equations, carlo miranda uses term region identify open connected set, , reserves term domain identify internally connected, perfect set, each point of accumulation point of interior points, following former master mauro picone: according convention, if set region closure domain.








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