# 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: