Region (mathematical analysis)

In mathematical analysis, the word region usually refers to a subset of ${\displaystyle \mathbb {R} ^{n}}$ or ${\displaystyle \mathbb {C} ^{n}}$ that is open (in the standard Euclidean topology), connected and non-empty. A closed region is sometimes defined to be the closure of a region.

Regions and closed regions are often used as domains of functions or differential equations.

According to Kreyszig,

According to Yue Kuen Kwok,

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