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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
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 1991
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