Remarks on the behaviour of higher-order derivations on the gluing of differential spaces

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• 作者：Krzysztof Drachal
• 关键词：gluing of differential space ; higher ; order differential geometry ; Sikorski differential space ; 58A40
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：65
• 期：4
• 页码：1137-1154
• 全文大小：209 KB
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• 作者单位：Krzysztof Drachal (1)
  
  1. Faculty of Mathematics and Information Science, University of Warsaw, ul. Koszykowa 75, 00-662, Warszawa, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

This paper is about some geometric properties of the gluing of order k in the category of Sikorski differential spaces, where k is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour of k th order tangent spaces, their dimensions, and other geometric properties, are described in the context of the process of gluing differential spaces. At the end some examples are given. The paper is self-consistent, i.e., a short review of the differential spaces theory is presented at the beginning. Keywords gluing of differential space higher-order differential geometry Sikorski differential space