A continuum is a decomposable continuum if and only if it is the union of two of its proper subcontinua. A continuum that is not decomposable is an indecomposable continuum.
Decomposable Continuum
See also
Continuum, Hereditarily Decomposable Continuum, Indecomposable ContinuumThis entry contributed by Matt Insall (author's link)
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Insall, Matt. "Decomposable Continuum." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DecomposableContinuum.html