Integration on differential spaces

• Autorzy: Dziewa-Dawidczyk D. , Pasternak-Winiarski Z.
• Języki publikacji: EN

Abstrakty

EN

The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is given.

Słowa kluczowe

EN

differential space; integration

PL

przestrzeń różniczkowa; integracja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 748--762
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Dziewa-Dawidczyk D.

• Department of Applied Mathematics, Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences – SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland

autor

Pasternak-Winiarski Z.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
• Institute of Mathematics, University of Białystok Akademicka 2,15-267 Białystok, Poland

Bibliografia

• [1] D. Dziewa-Dawidczyk, Integration on differential spaces, (doctor thesis - in Polish), Warsaw University of Technology, Warsaw, 2010.
• [2] D. Dziewa-Dawidczyk, Z. Pasternak-Winiarski, On differential completions and compactifications of a differential space, Demonstratio Math. 45(4) (2012), 975–992; arXiv:1103.3597, 2011.
• [3] D. Dziewa-Dawidczyk, Z. Pasternak-Winiarski, Uniform structures on differential spaces , arXiv:1103.2799, 2011.
• [4] D. Dziewa-Dawidczyk, Z. Pasternak-Winiarski, Differential structures on natural bundles connected with a differential space, in "Singularities and Symplectic Geometry VII", Singularity Theory Seminar (2007), S. Janeczko (ed), Faculty of Mathematics and Information Science, Warsaw University of Technology.
• [5] R. Engelking, General Topology, PWN, Warsaw, 1975, (in Polish).
• [6] Z. Pasternak-Winiarski, Group differential structures and their basic properties, (doctor thesis - in Polish), Warsaw University of Technology, Warsaw, 1981.
• [7] W. Sasin, On some exterior algebra of differential forms over a differential space, Demonstratio Math. 19 (1986), 1063–1075.
• [8] R. Sikorski, Introduction to Differential Geometry, PWN, Warsaw, 1972, (in Polish).
• [9] W. Waliszewski, Regular and coregular mappings of differential space, Ann. Polon. Math. 30 (1975).