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

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Abstract

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.

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  1. Faculty of Mathematics and Information Science, University of Warsaw, ul. Koszykowa 75, 00-662, Warszawa, Poland

    Krzysztof Drachal

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  1. Krzysztof Drachal
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Correspondence to Krzysztof Drachal.

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The research funded by the Polish National Science Centre grant under the contract number DEC-2012/06/A/ST1/00256.

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Drachal, K. Remarks on the behaviour of higher-order derivations on the gluing of differential spaces. Czech Math J 65, 1137–1154 (2015). https://doi.org/10.1007/s10587-015-0232-z

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  • DOI: https://doi.org/10.1007/s10587-015-0232-z

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