2026-08-20T15:37:11Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/338722023-08-26T15:41:08Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Fernando Galván, José Francisco
2023-06-19T13:29:54Z
2023-06-19T13:29:54Z
2014-07
1474-7480
10.1017/S1474748014000206
https://hdl.handle.net/20.500.14352/33872
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9295148&fileId=S1474748014000206
http://arxiv.org/abs/1309.3743
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.
eng
On the substitution theorem for rings of semialgebraic functions
journal article
URL
https://docta.ucm.es/bitstreams/5ce1ec4d-1468-4253-9f0e-4460d8093748/download
File
MD5
fe442a20f521d2e96b3a492998443be7
431401
application/pdf
1309.3743v1.pdf