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Article Dans Une Revue Acta Mathematica Hungarica Année : 2010

Convergences, pretopologies and proximities induced by Cauchy and Riesz screens

Résumé

We answer a question of Császár [12]: under which conditions a given pretopological closure or proximity can be induced by a Cauchy structure? We give a characterization for these closures and proximities using properties of convergences and nasses [14] induced by Cauchy structures. We prove also that the set of Cauchy screens inducing a given reciprocal convergence structure is a non empty interval of the set of Cauchy screens equipped with the usual inclusion order.
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Dates et versions

hal-04090501 , version 1 (25-05-2023)

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M. Chicourrat. Convergences, pretopologies and proximities induced by Cauchy and Riesz screens. Acta Mathematica Hungarica, 2010, 128 (3), pp.199-220. ⟨10.1007/s10474-010-9133-7⟩. ⟨hal-04090501⟩
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