Abstract
Let x be a sequence taking values in a separable metric space and let I be an Fσδ-ideal on the positive integers (in particular, I can be any Erdős–Ulam ideal or any summable ideal). It is shown that the collection of subsequences of x which preserve the set of I-cluster points of x is of second category if and only if the set of I-cluster points of x coincides with the set of ordinary limit points of x; moreover, in this case, it is comeager. The analogue for I-limit points is provided. As a consequence, the collection of subsequences of x which preserve the set of ordinary limit points is comeager.
Original language | English |
---|---|
Pages (from-to) | 221-229 |
Number of pages | 9 |
Journal | Topology and its Applications |
Volume | 263 |
DOIs | |
Publication status | Published - 15 Aug 2019 |
Keywords
- Asymptotic density
- Erdős–Ulam ideal
- F-ideal
- Generalized density ideal
- Ideal cluster points
- Ideal limit points
- Meager set
- Summable ideal
ASJC Scopus subject areas
- Geometry and Topology