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 Rn 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 Rn×R. This endows Rn 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 Rn with its sheaf of semialgebraic functions.

gollark: If it's just counting changed pixels, surely you could do that faster than realtime.
gollark: What if you turn lights on or off, or wave around the camera, or something?
gollark: Wait, your lightning thing just counts whether a lot of pixels change between frames?
gollark: Multithreadedly find lightning frames, serially cluster them and generate the GIFs?
gollark: Leak them to other people via DM?

See also


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