A decomposition of a set definable in an o-minimal structure into perfectly situated sets

Wiesław Pawłucki. "A decomposition of a set definable in an o-minimal structure into perfectly situated sets." Annales Polonici Mathematici 79.2 (2002): 171-184. <http://eudml.org/doc/280203>.

@article{WiesławPawłucki2002,
abstract = {A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any two different sets of the decomposition are simply separated and their intersection is of dimension < k.},
author = {Wiesław Pawłucki},
journal = {Annales Polonici Mathematici},
keywords = {o-minimal structure; definable set; perfectly situated set; simple separation; Lipschitz mapping},
language = {eng},
number = {2},
pages = {171-184},
title = {A decomposition of a set definable in an o-minimal structure into perfectly situated sets},
url = {http://eudml.org/doc/280203},
volume = {79},
year = {2002},
}

TY - JOUR
AU - Wiesław Pawłucki
TI - A decomposition of a set definable in an o-minimal structure into perfectly situated sets
JO - Annales Polonici Mathematici
PY - 2002
VL - 79
IS - 2
SP - 171
EP - 184
AB - A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any two different sets of the decomposition are simply separated and their intersection is of dimension < k.
LA - eng
KW - o-minimal structure; definable set; perfectly situated set; simple separation; Lipschitz mapping
UR - http://eudml.org/doc/280203
ER -