论文标题
保留极限点的子序列和排列的Baire类别
The Baire Category of Subsequences and Permutations which preserve Limit Points
论文作者
论文摘要
令$ \ mathcal {i} $成为$ \ mathbf {n} $的微不足道的理想。我们表明，如果$ x $是一个在可分开的度量空间中的值的序列，则该子序列集。 $ x $的排列]保留$ \ MATHCAL {i} $的集合 - $ x $的群集点在拓扑上很大，并且仅当$ x $的每个普通限制点也是$ \ Mathcal {i} $ - $ x $的群集点。所有最大理想的模拟声明都失败了。这扩展了[拓扑应用程序的主要结果。 \ textbf {263}（2019），221--229]。作为一个应用程序，如果$ x $是一个在第一个可计数的紧凑型空间中具有值的序列，则为$ \ mathcal {i} $ - 收敛到$ \ ell $，则是子序列的集合[resp。排列]是$ \ MATHCAL {i} $ - 收敛到$ \ ell $在拓扑上是很大的，并且仅当$ x $从普通意义上收敛到$ \ ell $。对于$ \ Mathcal {i} $ - 限制点，提供$ \ Mathcal {i} $的类似结果是一个分析性p-ideal。
Let $\mathcal{I}$ be a meager ideal on $\mathbf{N}$. We show that if $x$ is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of $x$ which preserve the set of $\mathcal{I}$-cluster points of $x$ is topologically large if and only if every ordinary limit point of $x$ is also an $\mathcal{I}$-cluster point of $x$. The analogue statement fails for all maximal ideals. This extends the main results in [Topology Appl. \textbf{263} (2019), 221--229]. As an application, if $x$ is a sequence with values in a first countable compact space which is $\mathcal{I}$-convergent to $\ell$, then the set of subsequences [resp. permutations] which are $\mathcal{I}$-convergent to $\ell$ is topologically large if and only if $x$ is convergent to $\ell$ in the ordinary sense. Analogous results hold for $\mathcal{I}$-limit points, provided $\mathcal{I}$ is an analytic P-ideal.
