Ważewski universal dendrite

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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 $A$.

A Wazewski universal dendrite $D_{\omega}$


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


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


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