| 徐利治,徐铁生.Poincaré线性连续统直觉概念的公式化(英文)[J].数学研究及应用,2003,23(4):635~643 |
| Poincaré线性连续统直觉概念的公式化(英文) |
| A Formulation of Poincaré's Intuitive Concept of Linear Continuum |
| 投稿时间：2002-12-02 |
| DOI：10.3770/j.issn:1000-341X.2003.04.011 |
| 中文关键词: 内束 Poincaré连续统 跃距结构 半无限小 |
| 英文关键词:Poincaré's intimate bond leap-structure Poincaré continuum semi- infinitesimal. |
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| 中文摘要: |
| 本文研究了Poincaré著名注记中“内束”观念的数学表述法问题,通过构建Poincaré连续统模型,得到了这一问题的一种解答。文中还论述了有关数理哲学及方法论问题;文末特别指出了须继续研究的数学问题。 |
| 英文摘要: |
| Henri Poincaré's intuitive concept of the linear continuum was described by his famous remark which was noted by Bertrand Russell, and in which the notion of "intimate bond" first appeared. This semi-expository paper gives an exposition of Poincaré's remark, and also aims at a formulation of the intimate bond with the aid of introducing a kind of "leap structure" into Robinson's *R as a supplemental construction. As a result, we obtain a kind of hyperstandard model that may be called "Poincaré continuum". |
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