Revista de la
Unión Matemática Argentina
A connection between hyperreals and topological filters
Mohamed Benslimane

Volume 69, no. 1 (2026), pp. 155–160    

Published online (final version): December 19, 2025

https://doi.org/10.33044/revuma.4820

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Abstract

The aim of this paper is to show that the ultrapower $^\ast\mathbb{R}$ of the real line $\mathbb{R}$ 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 $\mathbb{R}$, viewed as a distributive lattice. Moreover, the topology induced on $^\ast\mathbb{R} \setminus \mathbb{R}$ through this embedding is separated (Hausdorff).

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