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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 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''n'' with its sheaf of semialgebraic functions.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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