Category theoretical view of I-cluster and I-limit points for ideals I with the baire property
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Date
2019
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Publisher
Maltepe Üniversitesi
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CC0 1.0 Universal
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info:eu-repo/semantics/openAccess
Abstract
We study the concept of I-cluster and I-limit points of a sequence, where I is an ideal with the Baire property. We obtain the relationship between I-cluster and I-limit points of subsequences of a given sequence in the sense of category. Our main result is Theorem Suppose s is a bounded sequence, L the set of its limit points and I is an ideal with the Baire property. Then the set of its subsequences with the same set of I-cluster points as s is co-meager if and only if all elements of L are I-cluster points of s, and is meager otherwise. The analogous statement also holds if I-limit points are in place of I-cluster points.
Description
Keywords
Ideal convergence, Subsequences, I-cluster and I-limit points
Journal or Series
International Conference of Mathematical Sciences (ICMS 2019)
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Citation
Wieren, L. M., Yurdakadim, T. ve Tas, E. (2019). Category theoretical view of I-cluster and I-limit points for ideals I with the baire property. International Conference of Mathematical Sciences (ICMS 2019). s. 79.
