We establish that the category of Cauchy spaces and Cauchy continuous maps upholds an intrinsic differentiation theory. Its intrinsic concept of smooth map differs from the usual one even on finite dimensional open domains. We also study a second category (proximeric spaces) for Cauchy continuous maps, showing it to be a topocosm (special quasitopos) with nice embedding of compact and precompact spaces.

Additional Metadata
Keywords Categorical differentiation theory, Cauchy spaces, Topocosm, Toponome
Persistent URL dx.doi.org/10.1016/0166-8641(93)90132-W
Journal Topology and its Applications
Citation
Bonenfant, P., & Nel, L. (1993). Categorical differentiation theory and Cauchy continuity. Topology and its Applications, 53(2), 119–130. doi:10.1016/0166-8641(93)90132-W