A generalization of the density zero ideal

2020/05/25 by Som, Sumit
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2005.12355

Abstract

Let \mathscrF=(F_n) be a sequence of nonempty finite subsets of ω such that lim_n |F_n|=∞ and define the ideal I(\mathscrF):=\A⊆ ω: |A∩ F_n|/|F_n|→ 0~as~n→ ∞ \. The case F_n=\1,…,n\ corresponds to the classical case of density zero ideal. We show that I(\mathscrF) is an analytic P-ideal but not F_σ. As a consequence, we show that the set of real bounded sequences which are I(\mathscrF)-convergent to 0 is not complemented in ℓ_∞.

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