The
*Cantor organ*
is the union of the product of the Cantor
ternary set and the unit interval and all segments
of the form
or
, where
(, resp.) is the closure of a component of
of length
(
),
[Kuratowski 1968, p. 191]. See Figure A.

- is an arc-like continuum which is irreducible between points and , where , and has exactly four end points.
- It has uncountably many arc components.

A variation of the Cantor organ is the
*Cantor accordion*
which is defined as the monotone
image of under a map that shrinks horizontal bars
and
to points [Kuratowski 1968, p.
191]. See Figure B.

Besides the above properties,

- has an upper semi-continuous monotone decomposition into arcs with the quotient space an arc.