Introduction to \(d\)-spaces theory. (English) Zbl 1298.58008

As a consequence of the endeavour of generalizing the differentiability to functions not necessarily defined in open subsets of numeric spaces, several notions of differential spaces appeared. The author discusses the notion first considered by R. Sikorski in [An introduction to differential geometry. (Wstȩp do geometrii różniczkowej.) Warszawa: Panstwowe Wydawnictwo Naukowe (1972; Zbl 0255.53001)], names these spaces “\(d\)-spaces” and presents some of their basic properties. He also investigates a glueing technique for these spaces and discusses the differential dimension. Finally he briefly presents some domains where this theory may be useful.


58A40 Differential spaces


Zbl 0255.53001