Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

Topology of Injective Endomorphisms of Real Algebraic Sets

Abstract : Using only basic topological properties of real algebraic sets and regular morphisms we show that any injective regular self-mapping of a real algebraic set is surjective. Then we show that injective morphisms between germs of real algebraic sets define a partial order on the equivalence classes of these germs divided by continuous semi-algebraic homeomorphisms. We use this observation to deduce that any injective regular self-mapping of a real algebraic set is a homeomorphism. We show also a similar local property. All our results can be extended to arc-symmetric semi-algebraic sets and injective continuous arc-symmetric morphisms, and some results to Euler semi-algebraic sets and injective continuous semi-algebraic morphisms.
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-00128201
Contributor : Import Arxiv Connect in order to contact the contributor
Submitted on : Wednesday, January 31, 2007 - 10:25:43 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:44 AM

Links full text

Identifiers

Collections

Citation

Adam Parusinski. Topology of Injective Endomorphisms of Real Algebraic Sets. Mathematische Annalen, Springer Verlag, 2004, 328, pp.353-372. ⟨hal-00128201⟩

Share

Metrics

Record views

68