A connection between hyperreals and topological filters

• Mohamed Benslimane ^[1]
  1. [1] Abdelmalek Essaˆadi University,Tetouan, Morocco
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 155-160
• Idioma: inglés
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• Resumen

  • The aim of this paper is to show that the ultrapower ∗R of the real line R with respect to a selective ultrafilter on the natural numbers (Choquet's absolute ultrafilter) can be naturally embedded in the prime spectrum of the usual topology on R, viewed as a distributive lattice. Moreover, the topology induced on ∗R∖R through this embedding is separated (Hausdorff).