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SEMINAR ON DIFFERENTIAL SPACES

SEMINAR ON DIFFERENTIAL SPACES DEMONSTRATIO MATHEMATICAVol. XXIV No 3-41991SEMINAR ON DIFFERENTIAL SPACESThe concept of differentiable manifold remains crucial inmodelling many physical phenomena; in particular space-timesof all major physical theories are supposed to share properties of a sufficiently smooth manifold. However, in some areasof research there is the necessity to go beyond this assumption. For instance, there are poor reasons for supporting theview that, in the quantum gravity regime of the very earlyUniverse, the differentiable manifold structure will continueto play its role as an arena for physical processes. And evenin classical singularities (i.e. without taking into accountany quantum gravity effects) the manifold structure is expected to brake down. The high degree of homogeneity, inherent inthe manifold concept, seem to be both very limiting and, insome cases, quite arbitrary assumption.When giving up the locally Euclidean character of physicalspaces, their numerical description must be preserved, i.e.the one in terms of real numbers or real valued functions.This is because all measurement results are always given asreal numbers.In the beginning of the sixties the idea was born to systematically investigate possible generalizations of the manifoldconcept.ThissuggestionwasspelledoutbyA. Grothendick, and was first discussed among mathematiciansworking in the field of algebraic geometry. Some mathematicians took over the idea, and several similar concepts http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

SEMINAR ON DIFFERENTIAL SPACES

Demonstratio Mathematica , Volume 24 (3-4): 2 – Jul 1, 1991

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Publisher
de Gruyter
Copyright
© 2017
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1991-3-402
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXIV No 3-41991SEMINAR ON DIFFERENTIAL SPACESThe concept of differentiable manifold remains crucial inmodelling many physical phenomena; in particular space-timesof all major physical theories are supposed to share properties of a sufficiently smooth manifold. However, in some areasof research there is the necessity to go beyond this assumption. For instance, there are poor reasons for supporting theview that, in the quantum gravity regime of the very earlyUniverse, the differentiable manifold structure will continueto play its role as an arena for physical processes. And evenin classical singularities (i.e. without taking into accountany quantum gravity effects) the manifold structure is expected to brake down. The high degree of homogeneity, inherent inthe manifold concept, seem to be both very limiting and, insome cases, quite arbitrary assumption.When giving up the locally Euclidean character of physicalspaces, their numerical description must be preserved, i.e.the one in terms of real numbers or real valued functions.This is because all measurement results are always given asreal numbers.In the beginning of the sixties the idea was born to systematically investigate possible generalizations of the manifoldconcept.ThissuggestionwasspelledoutbyA. Grothendick, and was first discussed among mathematiciansworking in the field of algebraic geometry. Some mathematicians took over the idea, and several similar concepts

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1991

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