论文标题
密度为零理想的概括
A generalization of the density zero ideal
论文作者
论文摘要
令$ \ Mathscr {f} =（f_n）$为$ω$的一系列非空的有限子集，使得$ \ lim_n | f_n | = \ infty $并定义了理想的$ \ mathcal {i}（i} f_n |/| f_n | \ to 0〜 \ mbox {as} 〜n \ to \ infty \ right \}。我们表明，$ \ Mathcal {i}（\ Mathscr {f}）$是一个分析性的p-思想，但不是$f_σ$。结果，我们表明，$ \ MATHCAL {i}（\ MATHSCR {f}）$ - 收敛到$ 0 $的真实有限序列集未用$ \ ell_ \ infty $补充。
Let $\mathscr{F}=(F_n)$ be a sequence of nonempty finite subsets of $ω$ such that $\lim_n |F_n|=\infty$ and define the ideal $$\mathcal{I}(\mathscr{F}):=\left\{A\subseteq ω: |A\cap F_n|/|F_n|\to 0~\mbox{as}~n\to \infty \right\}.$$ The case $F_n=\{1,\ldots,n\}$ corresponds to the classical case of density zero ideal. We show that $\mathcal{I}(\mathscr{F})$ is an analytic P-ideal but not $F_σ$. As a consequence, we show that the set of real bounded sequences which are $\mathcal{I}(\mathscr{F})$-convergent to $0$ is not complemented in $\ell_\infty$.
