# Omiljanowski dendrite

The Omiljanowski dendrite, usually denoted \$L_0\$, is the following dendrite:

# Properties

Theorem: All ramification points of \$L_0\$ are of order 3.

Proof:

Theorem: The set \$R(L_0)\$ of all ramification points of \$L_0\$ is discrete (hence nowhere dense).

Proof:

Theorem: For each maximal arc \$A\$ in \$L_0\$ the closure of the set \$A \cap R(L_0)\$ contains a homeomorphic copy of the Cantor set.

Proof:

Theorem: \$L_0\$ is monotonically equivalent to the dendrite \$D_3\$.

Proof: