Abstract
For a constructive-axiomatic approach to general relativistic spacetime, a mathematical theory of contact structures has been developed (cf. Mayr (1983)). Roughly, contact structures characterize at a very basic level a concept of tangentia- bility related to mathematical objects like sets, relations or maps. And—as a consequence of the general level—contact structures transport the concept of differentiability from normed vector or Banach spaces to suitable uniform spaces (pregeodesic contact spaces).
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References
Bourbaki, N.: 1966, ‘Elements of Mathematics. General Topology’, Herman, Paris.
Bourbaki, N.: 1968, ‘Elements of Mathematics. Theory of Sets ’, Herman, Paris.
Bourbaki, N.: 1971, ‘Éléments de Mathématique. Variétés différentielles et analytiques’ Herman, Paris.
Dieudonné, J. 1969, ‘Foundations of Modern Analysis’, Academic Press, New York.
Mayr, D.: 1983, ‘Zur konstruktiv-axiomatischen Charakteri- sierung der differenzierbaren Struktur in der allgemeinen Raumzeit durch das Prinzip der approximativen Reproduzier- barkeit’, Habilitationsschrift, presented to the Fachbe- reich Physik der Universitat Marburg.
Schaefer, H. H.: 1971, ‘Topological Vector Spaces’, Springer, New York.
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© 1984 D. Reidel Publishing Company, Dordrecht, Holland
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Mayr, D. (1984). Contact Structures, Predifferentiability and Approximation. In: Balzer, W., Pearce, D.A., Schmidt, HJ. (eds) Reduction in Science. Synthese Library, vol 175. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6454-9_10
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DOI: https://doi.org/10.1007/978-94-009-6454-9_10
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