In mathematical analysis, the word * region* usually refers to a subset of or that is open (in the standard Euclidean topology), simply connected and non-empty. A

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

According to Kreyszig,

- A region is a set consisting of a domain plus, perhaps, some or all of its boundary points. (The reader is warned that some authors use the term "region" for what we call a domain [following standard terminology], and others make no distinction between the two terms.)
^{[1]}

According to Yue Kuen Kwok,

- An open connected set is called an
*open region*or*domain*. ...to an open region we may add none, some, or all its limit points, and simply call the new set a*region*.^{[2]}

- Area
- Curve
- Interval (mathematics)
- Jordan curve theorem
- Locus (mathematics)
- Neighbourhood (mathematics)
- Point (geometry)
- Riemann mapping theorem
- Shape

- Ruel V. Churchill (1960)
*Complex variables and applications*, 2nd edition, ยง1.9 Regions in the complex plane, pp. 16 to 18, Regions and closed regions are often used as domains of functions or differential equations.According to Kreyszig,

According to Yue Kuen Kwok,

- An open connected set is called an
*open region*or*domain*. ...to an open region we may add none, some, or all its limit points, and simply call the new set a*region*.^{[2]}

## See also

- An open connected set is called an