Abstract
AbstractWe show that an ideal $$\mathcal {I}$$
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 $$\mathcal {I}$$
I
-limit points is comeager and, in addition, every accumulation point of x is also an $$\mathcal {I}$$
I
-limit point (that is, a limit of a subsequence $$(x_{n_k})$$
(
x
n
k
)
such that $$\{n_1,n_2,\ldots ,\} \notin \mathcal {I}$$
{
n
1
,
n
2
,
…
,
}
∉
I
). The analogous characterization holds also for $$\mathcal {I}$$
I
-cluster points.
Funder
Università degli Studi dell’Insubria
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis