Abstract: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).
Keywords: P-ideal; nowhere dense set; extension; analytic ideal; maximal ideal; meager ideal; ideal convergence
AMS Subject Classification: 54D35 54G10 54D80 40A05 40A35