## Całkowanie na przestrzeniach różniczkowych

### Diana Dziewa-Dawidczyk

#### Abstract

Standard integration theory could be trivial for some differential spaces. For instance if ' is a smooth cube any dimension k on the differential space M = (Qk,C1(Rk)Qk ), where Q is set of rational number and ! is any continuous point k-form on M, than R ' ! = 0. In that thesis there is such a generalization of the integration theory, in which there are cubes and chains, such that integrals of smooth differential forms in general are not 0. There are generalizations of n-dimensional cube, n-dimensional chain, and exterior derivative. In that paper there is the analogue of Stokes theorem for the differential spaces. In that thesis the theory of the uniform spaces and the theory of completions and compactifications are described. They were use as tools for generalization of the integration theory.Diploma type | Doctor of Philosophy | ||||

Author |
Diana Dziewa-Dawidczyk (FMIS)
Diana Dziewa-Dawidczyk
| ||||

Title in Polish | Całkowanie na przestrzeniach różniczkowych | ||||

Language | pl polski | ||||

Certifying Unit | Faculty of Mathematics and Information Science (FMIS) | ||||

Discipline | mathematics / (mathematics domain) / (physical sciences) | ||||

Defense Date | 18-11-2010 | ||||

Supervisor |
Zbigniew Pasternak-Winiarski (FMIS / DDG)
Zbigniew Pasternak-Winiarski
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Internal reviewers |
Wiesław Sasin (FMIS / DDG)
Wiesław Sasin
| ||||

External reviewers |
Aleksy Tralle - [Uniwersytet Warmińsko-Mazurski w Olsztynie]
Aleksy Tralle
- Uniwersytet Warmińsko-Mazurski w Olsztynie | ||||

Pages | 83 | ||||

Keywords in English | xxx | ||||

Abstract in English | Standard integration theory could be trivial for some differential spaces. For instance if ' is a smooth cube any dimension k on the differential space M = (Qk,C1(Rk)Qk ), where Q is set of rational number and ! is any continuous point k-form on M, than R ' ! = 0. In that thesis there is such a generalization of the integration theory, in which there are cubes and chains, such that integrals of smooth differential forms in general are not 0. There are generalizations of n-dimensional cube, n-dimensional chain, and exterior derivative. In that paper there is the analogue of Stokes theorem for the differential spaces. In that thesis the theory of the uniform spaces and the theory of completions and compactifications are described. They were use as tools for generalization of the integration theory. | ||||

Thesis file |
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Citation count* | 5 (2020-09-26) |

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