# Hereditarily unicoherent

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

# Properties

## Theorem

If $X$ be a tree-like continuum, then $X$ is hereditarily unicoherent.

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

If $X$ be a tree-like continuum, then $X$ is hereditarily unicoherent.