Closure sets of functions and a hierarchy of filters

Mignone, Robert

doi:10.1090/S0002-9939-1992-1070526-4

Closure sets of functions and a hierarchy of filters
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Proc. Amer. Math. Soc. 114 (1992), 799-807 Request permission

Abstract:

This paper presents a transfinite extension of a filter generating closure property of functions. One consequence of this extension is a hierarchy of filters which coincide with filters generated by a directed set type closure property. At each level of this hierarchy a progressively stronger notion of normality is satisfied. Ideals with this stronger notion of normality each have a corresponding saturation characterization.

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