Limit points of subsequences

Paolo Leonetti

Research output: Contribution to journalArticleResearchpeer-review

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 languageEnglish
Pages (from-to)221-229
Number of pages9
JournalTopology and its applications
Volume263
DOIs
Publication statusPublished - 15 Aug 2019

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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

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