A continuum is a compact connected metric space; a dendroid is an arcwise hereditary unicoherent continuum. Given a continuum X, we denote by

2X = { A ⊂ X : A is closed and  A ≠ ∅ },

C(X) = { A ∈ 2X  : A is connected},

A selection is a continuous map s : C(X) → X satisfying that  s(A) ∈ A,  A ∈ C(X).
In this talk will go carefully through the above definitions and we will give several examples, then we will be able to define open selections by solving the problem of how to send open maps from n-cells to trees.

In this talk we show a way of constructing open maps from n-cells onto trees. The construction of these maps are very geometrical and only the notion of map and open set is needed to understand the main construction of this talk. We use this construction to construct open selections on n-ods.

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A 2-cell is the space [0,1] x [0,1] in general an n-cell is the space [0,1] x [0,1] … [0,1] (n times); an open map is a continuous function that sends open sets into open sets. An n-od is the union of 3 arcs intersecting in one point, ( which is an end point in each arc)  and a tree is the union of intervals that intersect only at its end points and do not have cycles.