No topologies characterize differentiability as continuity
Authors: Robert Geroch, Erwin Kronheimer and George McCarty
Journal: Proc. Amer. Math. Soc. 28 (1971), 273-274
MSC: Primary 57.20; Secondary 26.00
MathSciNet review: 0271969
Abstract: Do there exist topologies and for the set of real numbers such that a function from to is smooth in some specified sense (e.g., differentiable, , or ) with respect to the usual structure of the real line if and only if is continuous from to ? We show that the answer is no.