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Quelques propriétés des applications analytiques près d'un homéomorphisme

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Riassunto

Scopo di questo lavoro è iniziare lo studio della applicazioni analitiche od algebriche che sono vicine ad omeomorfismi. Nel paragrafo 1 si danno esempi di tali applicazioni e nel paragrafo 2 si prova, tra l'altro, il risultato seguente:

Sia ϕ:V→W un'applicazione analitica fra varietà analitiche reali connesse compatte; se:

  1. i)

    ϕ*:H *(V,Z2)→H *(W,Z 2) è un isomorfismo;

  2. ii)

    esiste un insieme analitico proprioS⊂V tale che ϕ:V−S→W−ϕ(S) sia un omeomorfismo, allora ϕ è un omeomorfismo.

Résumé

Le but de ce travail c'est de commencer l'étude des applications analytiques ou algébriques qui sont proches des homéomorphismes. Dans le § 1 on donne des exemples à ce sujet et dans le § 2 on prouve, entre autre, le résultat suivant:

Soit ϕ:V→W une application analytique entre deux variétés analytiques réelles, connexes et compactes; si:

  1. i)

    ϕ:V-S→W-ϕ(S) est un isomorphisme;

  2. ii)

    il existe un ensemble analytique propreS⊂V tel que ϕ:V−S→W−ϕ(S) est un homéomorphisme, alors ϕ est un homéomorphisme.

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Authors and Affiliations

  1. Istituto Matematico, Via Machiavelli 35, 444100, Ferrara

    Lucia Beretta

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  1. Lucia Beretta
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Beretta, L. Quelques propriétés des applications analytiques près d'un homéomorphisme. Ann. Univ. Ferrara 30, 41–51 (1984). https://doi.org/10.1007/BF02853268

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  • DOI: https://doi.org/10.1007/BF02853268

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