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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).

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The topology of open semi-algebraic sets (appl.: totally positive matrices)

The homotopy groups of the semigroup of determinant one totally positive matrices are all trivial. A proof of this is in the paper (example 6.2) A. J. Santana and L.A.B. San Martin: The homotopy type …
Luiz San Martin's user avatar