For a given nonempty set we denote by any dendrite satisfying the following two conditions:

- (a)
- if is a ramification point of , then ;
- (b)
- for each arc contained in and for every there is in a point with .

The following properties of dendrites are known (see [Charatonik W.J. et al. 1994, Theorems 6.4 and 6.6-6.8, p. 230; Corollary 6.10, p. 232]).

- For any nonempty subset , the dendrite is strongly pointwise self-homeomorphic.
- If , then the dendrite is universal for the family of all dendrites.
- If the set is finite with , then is universal for the family of all dendrites having orders of ramification points at most .
- If the set is infinite and , then is universal for the family of all dendrites having finite orders of ramification points.
- Nonconstant open images of standard universal dendrites are homeomorphic to if and only if is a nonempty subset of .
- For any nonempty subset and for an arbitrary dendrite there exists a monotone mapping from onto , [Charatonik et al. 1998, Theorem 2.22, p. 239].
- For any nonempty subset the dendrite is monotonely homogeneous, [Charatonik 1996, Theorem 3.3, p. 292].