歐氏空間在豪斯多夫距離下集合級數絕對收斂 之研究

Euclidean Space Absolutely Convergent Series of Sets Under Hausdorff Distance

李俊霖(Chun-Lin Li)

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/cycu201200164

摘要

本篇論文主要探討在歐氏空間下, 以豪斯多夫距離定義兩個集合之距離,來探討集合級數的收斂性之條件, 且推廣到一維度滿足柯西條件也會收斂,和收斂也會滿足柯西條件, 並且也滿足絕對收斂一定收斂. 我們定義在歐氏空間什麼是正向級數並且會和一維度的正向級數有相同的結果, 也就是說絕對收斂和收斂是等價.

關鍵字

柯西條件 ； 絕對收斂 ； 集合級數

並列摘要

The aim of the paper is to discuss the condition of convergence of series of sets between two sets which are defined under Hausdorff distance in Euclidean space. And we extended one-dimention series of sets for Cauchy condition converges and satisfies that every absolutely convergent series converges. In the end of the paper, we define the positive series in Euclidean
space, and the positive series have the same results with one dimention positive series, which means the absolutely convergent series of
sets is equivalent to convergent series of sets.

並列關鍵字

Series of stes ； Absolutely convergent ； Cauchy condition

參考文獻

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參考文獻