A continuum is hereditarily decomposable if each of its subcontinua is decomposable. An interval is hereditarily decomposable, as is a circle, whereas the buckethandle (also known as the Brouwer-Janiszewski-Knaster continuum) is indecomposable, and hence is not hereditarily decomposable.
Hereditarily Decomposable Continuum
See also
Continuum, Decomposable Continuum, Indecomposable ContinuumThis entry contributed by Matt Insall (author's link)
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References
Charatonik, J. J. "Means on Arc-Like Continua." http://web.umr.edu/~continua/4_Bubu.pdf.Charatonik, J. J. and Prajs, J. R. "On Local Connectedness of Absolute Retracts." Pac. J. Math. 201, 83-88, 2001.Kuratowski, K. Topology, Vol. 2. New York: Academic Press, 1968.Referenced on Wolfram|Alpha
Hereditarily Decomposable ContinuumCite this as:
Insall, Matt. "Hereditarily Decomposable Continuum." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HereditarilyDecomposableContinuum.html