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.
Originalsprache | englisch |
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Seiten (von - bis) | 221-229 |
Seitenumfang | 9 |
Fachzeitschrift | Topology and its Applications |
Jahrgang | 263 |
DOIs | |
Publikationsstatus | Veröffentlicht - 15 Aug. 2019 |
ASJC Scopus subject areas
- Geometrie und Topologie