Spaces with differential structure and an application to cosmology (Q2725247)

A common generalization under the term \(F\)-structured space of \textit{R. Sikorski}'s differential structures [Colloq. Math. 18, 251-272 (1967; Zbl 0162.25101)], \textit{W. Sasin}'s sheaf structured spaces [Demonstration Math. 24, No.~3-4, 601-634 (1991; Zbl 0786.58004)] and \textit{A. Fröhlicher}'s smooth spaces [\textit{A. Frölicher} and \textit{A. Kriegl}, `Linear Spaces and differentiation theory', Wiley-Interscience, Chichester (1988; Zbl 0657.46034)], the well-known generalizations of manifolds, is here considered. Actually, \(F\)-structured spaces are the structured spaces each open subset of which possesses a coherent Frölicher structure. Several relations among the resulting categories are studied and particular attention is paid to cartesian closedness as well as to the property of being topological over \({\mathcal S}et\). The former is used in a Frölicher space but not of necessity in a structured space model of the formalism for Robertson-Walker cosmology [\textit{R. M. Wald}, `General relativity,' Univ. Chicago Press, Chicago, IL. (1984; Zbl 0549.53001)].