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Results tagged with real-algebraic-geometry
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user 43054
Real algebraic geometry is the study of real solutions to algebraic equations with real coefficients. Its methods are rather different from classical algebraic geometry, which is typically done over an algebraically closed field (like the complex numbers).
12
votes
Accepted
General Tarski-Seidenberg Theorem
The most abstract version of the Tarski-Seidenberg theorem I know of is the following
Let $f:A\to B$ be a morphism of finite presentation of commutative rings. Then the induced map
$$f^*:\operatornam …
- 16.5k
13
votes
Accepted
What is the topology on the set of field orders
The topology you are looking for is called the Harrison topology. If we denote the set of ordering of a field $F$ with $\mathrm{Sper}\,F$ (more on that in a moment), this is the subspace topology give …
- 16.5k
5
votes
0
answers
92
views
Smoothness for real closed spaces
Is there a notion of smoothness for maps of real closed spaces in the sense of Schwartz? [1]
Ideally it would have the following properties:
Every smooth map of real closed spaces is locally of the …
- 16.5k
4
votes
0
answers
120
views
Semi-algebraic approximation of maps
These are really two questions but I hope that the same method will solve both of them.
For the purpose of this question let us fix a real closed field $R$, a bounded semialgebraic set $X$ over $R$, …
- 16.5k