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terminal continuum

A proper subcontinuum K$ of a continuum X$ is said to be a terminal continuum of X$ provided that if whenever A$ and B$ are proper subcontinua of X$ having union equal to X$ such that A\cap K \ne \emptyset \ne B \cap K$, then either X=A\cup K$ or X=B\cup K$.
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Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30