# Ważewski universal dendrite

A *Ważewski universal dendrite* is a dendrite $D_{\omega}$ with the property that each ramification point of $D_{\omega}$ is of order $\omega$ and for each arc $A \subset D_{\omega}$, the set of ramification points of $D_{\omega}$ which belong to $A$ is dense in $A$.

# Properties

**Theorem:** $D_{\omega}$ is universal in the class of all dendrites.

**Proof:** █

**Theorem:** $D_{\omega}$ is embeddable in the plane.

**Proof:** █

**Theorem:** Each open image of $D_{\omega}$ is homeomorphic to $D_{\omega}$.

**Proof:** █