Integration on differential spaces. (English) Zbl 1322.58006
Differential forms on differential spaces have been introduced since the ’80s. In the relevant works, tangent spaces are considered as spaces either of derivations [A. Kowalczyk, Demonstr. Math. 13, 893–905 (1980; Zbl 0477.58005); W. Sasin, Demonstr. Math. 19, 1063–1075 (1986; Zbl 0636.58007)], or of classes of equivalent curves [R. Mąka and P. Urbański, Demonstr. Math. 27, No. 1, 99–108 (1994; Zbl 0818.58006)]. In the latter work, generalizations of Stokes theorem and the Poincaré lemma have been proven.
The present authors consider differential forms on spaces of derivations, in the context of differential spaces, and they provide a generalization of integration theory of skew-symmetric forms on cubes and chains, obtaining an analogue of Stokes theorem.
The present authors consider differential forms on spaces of derivations, in the context of differential spaces, and they provide a generalization of integration theory of skew-symmetric forms on cubes and chains, obtaining an analogue of Stokes theorem.
Reviewer: Maria H. Papatriantafillou (Athenai)
MSC:
| 58A40 | Differential spaces |
| 58C35 | Integration on manifolds; measures on manifolds |
| 26A18 | Iteration of real functions in one variable |
References:
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| [3] | D. Dziewa-Dawidczyk, Z. Pasternak-Winiarski, Uniform structures on differential spaces , arXiv:1103.2799, 2011.; · Zbl 1322.58006 |
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