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

Krzysztof Drachal

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 4, page 1137-1154
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Drachal, Krzysztof. "Remarks on the behaviour of higher-order derivations on the gluing of differential spaces." Czechoslovak Mathematical Journal 65.4 (2015): 1137-1154. <http://eudml.org/doc/276054>.

@article{Drachal2015,
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 $k^\{\rm th\}$ 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.},
author = {Drachal, Krzysztof},
journal = {Czechoslovak Mathematical Journal},
keywords = {gluing of differential space; higher-order differential geometry; Sikorski differential space},
language = {eng},
number = {4},
pages = {1137-1154},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on the behaviour of higher-order derivations on the gluing of differential spaces},
url = {http://eudml.org/doc/276054},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Drachal, Krzysztof
TI - Remarks on the behaviour of higher-order derivations on the gluing of differential spaces
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 1137
EP - 1154
AB - 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 $k^{\rm th}$ 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.
LA - eng
KW - gluing of differential space; higher-order differential geometry; Sikorski differential space
UR - http://eudml.org/doc/276054
ER -

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