RT Journal Article
T1 On the substitution theorem for rings of semialgebraic functions
A1 Fernando Galván, José Francisco
AB Let R⊂F be an extension of real closed fields and S(M,R) the ring of (continuous) semialgebraic functions on a semialgebraic set M⊂Rn. We prove that every R-homomorphism φ:S(M,R)→F is essentially the evaluation homomorphism at a certain point p∈Fn \em adjacent \em to the extended semialgebraic set MF. This type of result is commonly known in Real Algebra as Substitution Theorem. In case M is locally closed, the results are neat while the non locally closed case requires a more subtle approach and some constructions (weak continuous extension theorem, \em appropriate immersion \em of semialgebraic sets) that have interest on their own. We afford the same problem for the ring of bounded (continuous) semialgebraic functions getting results of a different nature.
PB Cambridge Univ. Press
SN 1474-7480
YR 2014
FD 2014-07
LK https://hdl.handle.net/20.500.14352/33872
UL https://hdl.handle.net/20.500.14352/33872
LA eng
DS Docta Complutense
RD 18 abr 2025