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- W3200147434 abstract "Abstract We show that an ideal $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence x such that the set of subsequences [resp. permutations] of x which preserve the set of $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> -limit points is comeager and, in addition, every accumulation point of x is also an $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> -limit point (that is, a limit of a subsequence $$(x_{n_k})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> such that $${n_1,n_2,ldots ,} notin mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>{</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mo>}</mml:mo> <mml:mo>∉</mml:mo> <mml:mi>I</mml:mi> </mml:mrow> </mml:math> ). The analogous characterization holds also for $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> -cluster points." @default.
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- W3200147434 date "2023-03-27" @default.
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- W3200147434 title "Another characterization of meager ideals" @default.
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