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Hereditarily Unicoherent Continuum


Let X be a continuum (i.e., a compact connected metric space). Then X is hereditarily unicoherent provided that every subcontinuum of X is unicoherent.

HereditarilyUnicoherentContinuum

Any hereditarily unicoherent continuum is a unicoherent space, but there are unicoherent continua that are not hereditarily unicoherent. For example, the unit interval is hereditarily unicoherent, but a ray winding down on a circle is not hereditarily unicoherent, even though it is unicoherent. (This is due to the fact that a circle is not unicoherent.)


See also

Continuum, Unicoherent Space

This entry contributed by Matt Insall (author's link)

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Cite this as:

Insall, Matt. "Hereditarily Unicoherent Continuum." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HereditarilyUnicoherentContinuum.html

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