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中文摘要：
弗雷歇1906年的博士论文产生了极为重要的影响，而他在1904年和1905年的相关工作已经很好地勾勒出了其博士论文的轮廓。文章在原始文献的基础之上，对弗雷歇在抽象空间理论方面的最初工作进行了研究，进而揭示了这些工作对弗雷歇博士论文所产生的重要影响。同时，借助本文可以使我们更好地了解弗雷歇的工作方式，即追求“一般性”和“统一性”，这不但为我们做数学研究提供了一种可资借鉴的思路，也为我们反观20世纪数学发展的特征提供了一个窗口。
英文摘要：
Frechet＇ s doctoral thesis in 1906 had a very significant impact,and the related work he published in 1904 and 1905 had already sketched out a good deal of the groundwork of his thesis. Based on the original materials, this paper studies Frechet＇ s initial work toward abstract space theory, and reveals that the work of Frechet had an important impact on his doctoral thesis. Meanwhile, this paper can help us to understand better how Frechet worked pursuing ＂generalization＂ and ＂unity＂. This only offers us a helpful approach to study mathematics, but also provides a window to fully understand the characteristics of the development of the mathematics in the 20th century.
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