Pseudo-arc
The pseudo-arc is the only hereditarily indecomposable chainable continuum.
Properties
Being a pseudo-arc is a Whitney property
Being a pseudo-arc is a sequential strong Whitney-reversible property
References
A Note on an Unusual Characterization of the Pseudo-arc by Jan Van Mill
Drawing the pseudo-arc by Wayne Lewis and Piotr Minc
An introduction to some properties of the pseudo arc