# On semialgebraic points of definable sets

Banach Center Publications (1998)

- Volume: 44, Issue: 1, page 189-193
- ISSN: 0137-6934

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topPiękosz, Artur. "On semialgebraic points of definable sets." Banach Center Publications 44.1 (1998): 189-193. <http://eudml.org/doc/208882>.

@article{Piękosz1998,

abstract = {We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.},

author = {Piękosz, Artur},

journal = {Banach Center Publications},

keywords = {algebraic points; Tarski system; algebraic nonsingular points; definable set; o-minimal structure; analytic cell decomposition; semialgebraic points; degree of complexity},

language = {eng},

number = {1},

pages = {189-193},

title = {On semialgebraic points of definable sets},

url = {http://eudml.org/doc/208882},

volume = {44},

year = {1998},

}

TY - JOUR

AU - Piękosz, Artur

TI - On semialgebraic points of definable sets

JO - Banach Center Publications

PY - 1998

VL - 44

IS - 1

SP - 189

EP - 193

AB - We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.

LA - eng

KW - algebraic points; Tarski system; algebraic nonsingular points; definable set; o-minimal structure; analytic cell decomposition; semialgebraic points; degree of complexity

UR - http://eudml.org/doc/208882

ER -

## References

top- [1] J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. (3) 12, Springer, Berlin, 1987. Zbl0633.14016
- [2] L. van den Dries, C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540. Zbl0889.03025
- [3] S. Łojasiewicz, Ensembles semi-analytiques, Inst. de Hautes Études Scientifiques, Bures-sur-Yvette, 1965.

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