# Triod

From hyperspacewiki

A continuum $X$ is called a triod if there is a subcontinuum $Z$ of $X$ such that $X \setminus Z$ is the union of three nonempty sets each two of which are mutually separated in $X$. $X$ is called a weak triod if $X=X_1 \oplus X_2 \oplus X_3$ and $\bigcap_{i=1}^3 X_i = \emptyset$, where $\oplus$ denotes the essential sum.

# Properties

**Proposition:** Every triod is a weak triod.

**Proof:** █

**Theorem:** If $X$ is unicoherent, then $X$ is a triod if and only if $X$ is a weak triod.

**Proof:** █