Topology of Injective Endomorphisms of Real Algebraic Sets

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dc.creatorParusinski, Adam
dc.date2002-11-25
dc.date.accessioned2026-07-07T04:53:16Z
dc.date.available2026-07-07T04:53:16Z
dc.descriptionUsing 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.
dc.description16 pages, AMS-Latex
dc.identifierhttps://arxiv.org/abs/math/0211384
dc.identifierhttp://arxiv.org/abs/math/0211384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65777
dc.subjectAlgebraic Geometry
dc.subject14Pxx, 14A10, 32B10
dc.titleTopology of Injective Endomorphisms of Real Algebraic Sets
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