Probably the easiest example of a torsor to understand is the trivial torsor in the topological case.
Given a space and a sheaf of groups, on , the sheaf of sets underlying has a natural left action by , which is a sheaf morphism. This is transitive etc. and so gives a torsor, called the trivial -torsor, denoted .
It is very important to note that has non-empty (i.e., has a ‘global section’), since it is a group so must have an identity element. Conversely any -torsor which has such a ‘global section’ is isomorphic to .