Coordinate space in the context of Scalar (mathematics)

In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate space R or the complex coordinate space C. A connected open subset of coordinate space is frequently used for the domain of a function.

The basic idea of a connected subset of a space dates from the 19th century, but precise definitions vary slightly from generation to generation, author to author, and edition to edition, as concepts developed and terms were translated between German, French, and English works. In English, some authors use the term domain, some use the term region, some use both terms interchangeably, and some define the two terms slightly differently; some avoid ambiguity by sticking with a phrase such as non-empty connected open subset.

A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of the stimulus source. (In contrast, a color model defines a coordinate space to describe colors, such as the RGB and CMYK color models.)

A uniform color space (UCS) is a color model that seeks to make the color-making attributes perceptually uniform, i.e. identical spatial distance between two colors equals identical amount of perceived color difference. A CAM under a fixed viewing condition results in a UCS; a UCS with a modeling of variable viewing conditions results in a CAM. A UCS without such modelling can still be used as a rudimentary CAM.