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<p>We present a counterexample related to relative uniform convergence, showing that, in general, the relatve uniform completion of the principal ideal of a vector lattice <i>E</i> generated by an element <i>x</i> is stricly contained in the ideal generated by <i>x</i> in the relatively uniform completion of <i>E</i>.</p>

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A counterexample regarding the relatively uniform completion of a principal ideal.

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Youssef Azouzi

摘要

We present a counterexample related to relative uniform convergence, showing that, in general, the relatve uniform completion of the principal ideal of a vector lattice E generated by an element x is stricly contained in the ideal generated by x in the relatively uniform completion of E.