对“Lindelöf关于理想”的修正[新西兰数学学报,42,115-120,2012]

Q4 Mathematics
Jiarul Hoque, S. Modak
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引用次数: 0

摘要

在此修正中,我们给出了一个反例,说明在考虑Hamlett在他的论文“Lindelöf关于理想”中的命题“{\it if $f: X \to Y$ and ${\bf J}$是$Y$上的理想,那么$f^{-1}({\bf J}) = \{f^{-1}(J): J \in {\bf J}\}$是$X$}上的理想”时存在错误[新西兰数学学报,42,115-120,2012]。我们在这里也对它作了新的修改,从此正确地提出了基于其中所导出的上述陈述的所有结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Amendment to "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]
We give a counterexample in this amendment to show that there is an error in consideration of the statement "{\it if $f : X \to Y$ and ${\bf J}$ is an ideal on $Y$, then $f^{-1}({\bf J}) = \{f^{-1}(J) : J \in {\bf J}\}$ is an ideal on $X$}" by Hamlett in his paper "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]. We also modify it here in a new way and henceforth put forward correctly all the results that were based on the said statement derived therein.
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来源期刊
New Zealand Journal of Mathematics
New Zealand Journal of Mathematics Mathematics-Algebra and Number Theory
CiteScore
1.10
自引率
0.00%
发文量
11
审稿时长
50 weeks
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