Geodesic
Extending the ideal of nowhere dense subsets of rationals to a P-ideal
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 429-435.

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We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, $F_\sigma$ ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).
Classification : 40A05, 40A35, 54D35, 54D80, 54G10
Keywords: P-ideal; nowhere dense set; extension; analytic ideal; maximal ideal; meager ideal; ideal convergence 
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Filipów, Rafał; Mrożek, Nikodem; Recław, Ireneusz; Szuca, Piotr. Extending the ideal of nowhere dense subsets of rationals to a P-ideal. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 429-435. http://geodesic.mathdoc.fr/item/CMUC_2013__54_3_a8/