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We show that an ideal $mathcal{I}$ on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence $x$ such that the set of subsequences [resp. permutations] of $x$ which preserve the set of $mathcal{I}$-limit points is comeager and, in addition, every accumulation point of $x$ is also an $mathcal{I}$-limit point (that is, a limit of a subsequence $(x_{n_k})$ such that ${n_1,n_2,ldots,} otin mathcal{I}$). The analogous characterization holds also for $mathcal{I}$-cluster points.
The notion of Haar null set was introduced by J. P. R. Christensen in 1973 and reintroduced in 1992 in the context of dynamical systems by Hunt, Sauer and Yorke. During the last twenty years this notion has been useful in studying exceptional sets in
For a non-isolated point $x$ of a topological space $X$ the network character $nw_chi(x)$ is the smallest cardinality of a family of infinite subsets of $X$ such that each neighborhood $O(x)$ of $x$ contains a set from the family. We prove that (1) e
A {it weak selection} on $mathbb{R}$ is a function $f: [mathbb{R}]^2 to mathbb{R}$ such that $f({x,y}) in {x,y}$ for each ${x,y} in [mathbb{R}]^2$. In this article, we continue with the study (which was initiated in cite{ag}) of the outer measures $l
We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff space $X$ equipped with the topology of pointwise convergence is distinguished if and only if $X$ is a $Delta$-space in the sense of cite {Knight}. A
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to which subsequence of an ideal convergent sequence may fail to be ideal c