Indecomposable continuum

For the indecomposability attributed to the real line by constructive mathematics, see Indecomposability (constructive mathematics).
The first four stages of the construction of the bucket handle as the limit of a series of nested intersections

In point-set topology, an indecomposable continuum is a continuum that is indecomposable, i.e. that cannot be expressed as the union of any two of its proper subcontinua. In 1910, L. E. J. Brouwer was the first to describe an indecomposable continuum.

Indecomposable continua have been used by topologists as a source of counterexamples. They also occur in dynamical systems.