Semialgebraic space

In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set.
Definition.
Let "U" be an open subset of R"n" 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"n"×R. This endows R"n" with a sheaf formula_1 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 formula_2 which is locally isomorphic to R"n" with its sheaf of semialgebraic functions.