Unicoherent

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Let $K$ be a continuum. We say that $K$ is unicoherent if for all $A, B$ subcontinua of $K$, such that $A \bigcup B = K$, then intersection $A \bigcap B$ is connected.

Related definitions

  1. We say that a continuum $K$ is hereditarily unicoherent if every subcontinuum of $K$ is unicoherent.