The Borel complexity of ideal limit points

•Studying the Borel complexity of ideal limit points systematically.•Solving an open problem.•Revealing close connection of Borel complexity between ideal limit points and ideals. In this paper we mainly study the Borel complexity of ideal limit points, denoted by Λr(I), in a first countable space....

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Vydáno v:Topology and its applications Ročník 312; s. 108061
Hlavní autoři: He, Xi, Zhang, Hang, Zhang, Shuguo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.05.2022
Témata:
Borel complexity
Borel ideal
Farah ideal
Ideal cluster points
Ideal limit points
secondary
Borel ideal
Farah ideal
Ideal limit points
Borel complexity
Ideal cluster points
primary
ISSN:0166-8641
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Popis
Shrnutí:•Studying the Borel complexity of ideal limit points systematically.•Solving an open problem.•Revealing close connection of Borel complexity between ideal limit points and ideals. In this paper we mainly study the Borel complexity of ideal limit points, denoted by Λr(I), in a first countable space. We investigate the connection between complexity of Λr(I) and properties of the ideal I, and answer an open question. The main results are the following.•Fix a sequence r. Then Λr(I) can be any nonempty subset of ordinary limit points. This answers an open question. Moreover, under suitable assumptions, if the subset is Borel, then the corresponding ideal can be chosen to be Borel.•Λr(I) is closed for every real sequence r if and only if I is P+.•Λr(I) is Fσ for Farah ideals (a subclass of Fσδ ideals). These generalize several results in [1].
ISSN:0166-8641
DOI:10.1016/j.topol.2022.108061