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 typeDoctor of Philosophy
Author Diana Dziewa-Dawidczyk (FMIS)
Diana Dziewa-Dawidczyk,,
- Faculty of Mathematics and Information Science
Title in PolishCałkowanie na przestrzeniach różniczkowych
Languagepl polski
Certifying UnitFaculty of Mathematics and Information Science (FMIS)
Disciplinemathematics / (mathematics domain) / (physical sciences)
Defense Date18-11-2010
Supervisor Zbigniew Pasternak-Winiarski (FMIS / DDG)
Zbigniew Pasternak-Winiarski,,
- Department of Differential Geometry

Internal reviewers Wiesław Sasin (FMIS / DDG)
Wiesław Sasin,,
- Department of Differential Geometry
External reviewers Aleksy Tralle - [Uniwersytet Warmińsko-Mazurski w Olsztynie]
Aleksy Tralle,,
-
- Uniwersytet Warmińsko-Mazurski w Olsztynie
Pages83
Keywords in Englishxxx
Abstract in EnglishStandard 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
Dziewa-Dawidczyk.pdf 457.73 KB
Citation count*5 (2020-09-26)

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