Geodesic
Triangulation in o-minimal fields with standard part map
Lou van den Dries1 ; Jana Maříková2
1 Department of Mathematics, UIUC 1409 W. Green Street Urbana, IL 61801, U.S.A.
2 Department of Mathematics, WIU 476 Morgan Hall, 1 University Circle Macomb, IL 61455, U.S.A.
Fundamenta Mathematicae, Tome 209 (2010) no. 2, pp. 133-155

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let $R$ be an o-minimal field with a proper convex subring $V$, and let $\mathop{\rm st}: V \to \boldsymbol k$ be the corresponding standard part map. Under a mild assumption on $(R,V)$ we show that a definable set $X\subseteq V^n$ admits a triangulation that induces a triangulation of its standard part $\mathop{\rm st} X\subseteq \boldsymbol k^n$.
DOI : 10.4064/fm209-2-3
Keywords: answering questions kov fund math prove triangulation result independent interest detail o minimal field proper convex subring mathop boldsymbol corresponding standard part map under mild assumption definable set subseteq admits triangulation induces triangulation its standard part mathop subseteq boldsymbol

Lou van den Dries 1 ; Jana Maříková 2

1 Department of Mathematics, UIUC 1409 W. Green Street Urbana, IL 61801, U.S.A.
2 Department of Mathematics, WIU 476 Morgan Hall, 1 University Circle Macomb, IL 61455, U.S.A. 
@article{10_4064_fm209_2_3,
     author = {Lou van den Dries and Jana Ma\v{r}{\'\i}kov\'a},
     title = {Triangulation in o-minimal fields with standard part map},
     journal = {Fundamenta Mathematicae},
     pages = {133--155},
     publisher = {mathdoc},
     volume = {209},
     number = {2},
     year = {2010},
     doi = {10.4064/fm209-2-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm209-2-3/}
}
TY  - JOUR
AU  - Lou van den Dries
AU  - Jana Maříková
TI  - Triangulation in o-minimal fields with standard part map
JO  - Fundamenta Mathematicae
PY  - 2010
SP  - 133
EP  - 155
VL  - 209
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm209-2-3/
DO  - 10.4064/fm209-2-3
LA  - en
ID  - 10_4064_fm209_2_3
ER  - 
%0 Journal Article
%A Lou van den Dries
%A Jana Maříková
%T Triangulation in o-minimal fields with standard part map
%J Fundamenta Mathematicae
%D 2010
%P 133-155
%V 209
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm209-2-3/
%R 10.4064/fm209-2-3
%G en
%F 10_4064_fm209_2_3
Lou van den Dries; Jana Maříková. Triangulation in o-minimal fields with standard part map. Fundamenta Mathematicae, Tome 209 (2010) no. 2, pp. 133-155. doi: 10.4064/fm209-2-3

Cité par Sources :