Page "Differential topology" Paragraph 7

Consider the example of a coffee cup and a donut ( see < span class =" plainlinks "> this example </ span >).

From the point of view of differential topology, the donut and the coffee cup are the same ( in a sense ).

This is an inherently global view, though, because there is no way for the differential topologist to tell whether the two objects are the same ( in this sense ) by looking at just a tiny ( local ) piece of either of them.

He must have access to each entire ( global ) object.