Some properties of the polynomially bounded o-minimal expansions of the real field and of some quasianalytic local rings

Array

Authors

  • M. Berraho Ibn Tofail University, PO Box 242, Kenitra, Morocco

DOI:

https://doi.org/10.15330/cmp.12.2.483-491

Keywords:

Weierstrass division theorem, polynomially bounded o-minimal structure, quasianalytic ring, $(x_1)$-adic topology

Abstract

In this paper, we study the Weierstrass division theorem over the rings of smooth germs that are definable in an arbitrary polynomially bounded o-minimal expansion of the real field by giving some criteria for satisfying this theorem. Afterwards, we study some topological properties of some quasianalytic subrings of the ring of smooth germs for the $(x_1)$-adic topology by showing that these rings are separable metric spaces. Also, we cite a criterion for their completeness with respect to the $(x_1)$-adic topology.

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Published

2020-12-30

How to Cite

(1)
Berraho, M. Some Properties of the Polynomially Bounded O-Minimal Expansions of the Real Field and of Some Quasianalytic Local Rings: Array. Carpathian Math. Publ. 2020, 12, 483-491.

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Section

Scientific articles