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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Closure sets of functions and a hierarchy of filters


Author: Robert Mignone
Journal: Proc. Amer. Math. Soc. 114 (1992), 799-807
MSC: Primary 03E05
DOI: https://doi.org/10.1090/S0002-9939-1992-1070526-4
MathSciNet review: 1070526
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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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DOI: https://doi.org/10.1090/S0002-9939-1992-1070526-4
Article copyright: © Copyright 1992 American Mathematical Society

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