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We prove that in some families of planar rational compacta there are no universal elements.
We define a dendrite which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite of order n described by J. J. Charatonik.
In this paper we consider rational subspaces of the plane. A rational space is a space which has a basis of open sets with countable boundaries. In the special case where the boundaries are finite, the space is called rim-finite.
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