一个广义度量结构的压缩
Contraction of a Generalized Metric Structure
摘要：
在某些科学领域，缩放能够修改观察对象的拓扑结构。我们在目前的工作中的目标是引入一个新的形式主义适应这种现象的数学表示。为此，我们引入了一个新的度量结构-银河空间-它依赖于R的一个序域扩张。此外，银河空间范畴的某些自然变换，即收缩，特别令人感兴趣：它们推广了通常的同素性，它们具有可能是无穷小的比率，它们能够修改拓扑，并且它们满足一个很好的合成规则。借助于非标准扩张，我们可以把任何度量空间联系到一个无限族的星系空间，最后，我们研究了这个族的一些极限性质。
英文摘要：
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a new metric structure - the galactic spaces - which depends on an ordered field extension of R. Moreover, some natural transformations of the category of galactic spaces, the contractions, are of particular interest: they generalize usual homotheties, they have a ratio which may be an infinitesimal, they are able to modify the topology and they satisfy a nice composition rule. With the help of nonstandard extensions we can associate to any metric space an infinite family of galactic spaces; lastly, we study some limit properties of this family.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
