In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set.
Let U be an open subset of R<sup>n</sup> for some n. A semialgebraic function on U is defined to be a continuous real-valued function on U whose restriction to any semialgebraic set contained in U has a graph which is a semialgebraic subset of the product space R<sup>n</sup>ÃÂR. This endows R<sup>n</sup> with a sheaf of semialgebraic functions.
(For example, any polynomial mapping between semialgebraic sets is a semialgebraic function, as is the maximum of two semialgebraic functions.)
A semialgebraic space is a locally ringed space which is locally isomorphic to R<sup>n</sup> with its sheaf of semialgebraic functions.