Indecomposability

In constructive mathematics, indecomposability or indivisibility (German:Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces. This principle was established by Brouwer in 1928 using intuitionistic principles, and can also be proven using Church's thesis. The analogous property in classical analysis is the fact that any continuous function from the continuum to {0,1} is constant.