Given an ideal J on ω, we prove that a sequence in a topological space X is J -convergent if and only if there exists a "big" J -convergent subsequence. Then we study several properties and show two characterizations of the set of J -cluster points as classical cluster points of a filter on X and as the smallest closed set containing "almost all" the sequence. As a consequence, we obtain that the underlying topology τ coincides with the topology generated by the pair ( τ, J).

Characterizations of Ideal Cluster Points

Leonetti P
;
2019-01-01

Abstract

Given an ideal J on ω, we prove that a sequence in a topological space X is J -convergent if and only if there exists a "big" J -convergent subsequence. Then we study several properties and show two characterizations of the set of J -cluster points as classical cluster points of a filter on X and as the smallest closed set containing "almost all" the sequence. As a consequence, we obtain that the underlying topology τ coincides with the topology generated by the pair ( τ, J).
2019
2019
Ideal cluster point; ideal convergence; G-ideal; filter base; statistical convergence
Leonetti, P; Maccheroni, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142091
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