Frölicher versus Differential Spaces: A Prelude to Cosmology

Paul Cherenack
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Paul Cherenack: University of Cape Town, Department of Mathematics and Applied Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 391-413 from Springer

Abstract: Abstract Differential spaces due to R. Sikorski are compared with Frölicher spaces (earlier called smooth spaces and studied by A. Frölicher). The category of Frölicher spaces is known to be topological over sets and Cartesian closed under the usual set adjunction. We see that the category of differential spaces is topological over sets but not Cartesian closed under the usual set adjunction. The tangent and cotangent bundles of an arbitrary Frölicher space X are defined and these notions are seen to coincide with the usual ones if X is a smooth manifold. We show that one can define, in a fairly natural way, the notions metric, connection, Ricci tensor, Riemannian curvature tensor and finally Einstein tensor for an arbitrary Frölicher space.

Keywords: 18F15; 57R55; 58D15; Frölicher space; differential space; topological functor; Cartesian closed; tangent bundle; connection; Einstein tensor. (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_24

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DOI: 10.1007/978-94-017-2529-3_24

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