In 1966, J. Wolfgang Smith studied the following extension of the notion of a smooth manifold.
A differentiable structure on an arbitrary topological space is a family, , of real-valued functions on satisfying a certain closure condition.
To express the closure condition, we need an auxiliary notion. A plot of is a continuous map with domain an open subset of some Euclidean space with the property that for all .
The closure condition is that if a continuous map has the property that whenever is a plot for then then .
Revised on April 16, 2009 23:39:36
by Toby Bartels