Let I be a meager ideal on N. We show that if x is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of x which preserve the set of I-cluster points of x is topologically large if and only if every ordinary limit point of x is also an I-cluster point of x. The analogue statement fails for all maximal ideals. This extends the main results in [Topology Appl. 263 (2019), 221–229]. As an application, if x is a sequence with values in a first countable compact space which is I-convergent to ℓ, then the set of subsequences [resp. permutations] which are I-convergent to ℓ is topologically large if and only if x is convergent to ℓ in the ordinary sense. Analogous results hold for I-limit points, provided I is an analytic P-ideal.

The Baire Category of Subsequences and Permutations which preserve Limit Points

LEONETTI P
2020

Abstract

Let I be a meager ideal on N. We show that if x is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of x which preserve the set of I-cluster points of x is topologically large if and only if every ordinary limit point of x is also an I-cluster point of x. The analogue statement fails for all maximal ideals. This extends the main results in [Topology Appl. 263 (2019), 221–229]. As an application, if x is a sequence with values in a first countable compact space which is I-convergent to ℓ, then the set of subsequences [resp. permutations] which are I-convergent to ℓ is topologically large if and only if x is convergent to ℓ in the ordinary sense. Analogous results hold for I-limit points, provided I is an analytic P-ideal.
https://link.springer.com/article/10.1007/s00025-020-01289-y?wt_mc=Internal.Event.1.SEM.ArticleAuthorIncrementalIssue&utm_source=ArticleAuthorIncrementalIssue&utm_medium=email&utm_content=AA_en_06082018&ArticleAuthorIncrementalIssue_20201019#citeas
Analytic P-ideal; Ideal cluster points; Ideal convergence; Ideal limit points; Meager set; Permutations; Subsequences
Marek, Balcerzak; Leonetti, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142073
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