複數平面集合級數之阿貝耳審斂法

Complex Plane Abel’s Test for Series of Sets

楊佳樺(Chia-Hua Yang)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200163

摘要

本論文主要研究在複數空間下探討集合級數, 以豪斯多夫距離下之收斂性, 並推廣阿貝耳審斂法是否也適合在集合級數, 而阿貝耳審斂法是對此型態 ΣAnBn 來判斷其收斂性, 因此我們必須定義集合的相加和相乘, 在複數平面的集合相加和相乘是一個自然定義方式, 而我們也成功了把阿貝耳審斂法推廣到複數平面之集合級數, 這也是此篇論文之者要貢獻.

關鍵字

阿貝耳審斂法 ； 複數平面 ； 集合級數

並列摘要

We maimly discuss the convergence of series of sets in the complex space under the Hausdorff distance in this paper. And we extend the Abel’s test to the series of sets. The convergence on Abel’s test is considering ΣAnBn.
Therefore, we must define the addition and multiplication of series of sets, which is a natural definition in the complex plane. We also succeeded in applying Abel’s test to the series of sets in the complex plane. This is also
the main contribution in this paper.

並列關鍵字

Series of sets ； Abel’s test ； Complex plane

參考文獻

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參考文獻