In 1887–1894, Richard Dedekind explored a number of ideas within the project of placing mappings at the very center of pure mathematics. We review two such initiatives: the introduction in 1894 of groups into Galois theory intrinsically via field automorphisms, and a new attempt to define the continuum via maps from N to N (later called Baire space) in 1891. These represented the culmination of Dedekind’s efforts to reconceive pure mathematics within a theory of sets and maps and throw new light onto the nature of his structuralism and its specificity in relation to the work of other mathematicians.

中文翻译：

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戴德金的地图理论时期

1887 年至 1894 年，理查德·戴德金 (Richard Dedekind) 在将映射置于纯数学中心的项目中探索了许多想法。我们回顾了两个这样的创举：1894 年通过场自同构本质上将群引入伽罗瓦理论，以及在 1891 年通过从 N 到 N（后来称为贝尔空间）的映射来定义连续统的新尝试。这些代表了戴德金努力的顶峰在集合和映射理论中重新构思纯数学，并为他的结构主义的本质及其与其他数学家工作的特殊性提供新的思路。