Glasnik Matematicki, Vol. 38, No.1 (2003), 167-176.

DENDROIDS AND PREORDERS

Victor Neumann-Lara, Isabel Puga and Richard G. Wilson

Departamento de Matematicas, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico
e-mail: ipe@hp.fciencias.unam.mx

Departamento de Matematicas, Universidad Autonoma Metropolitana, Avenida San Rafael Atlixco, #186, Iztapalapa, Apartado Postal 55-532, C.P. 09340, Mexico, D.F., Mexico
e-mail: rgw@xanum.uam.mx

Abstract.   Let X be a dendroid and x* ∈ X. Δ₀(X, x*) will denote the preordered set of arc-components of X \ {x*}, where the preorder is defined by α ≤ β if α ⊆ cl(β). In this paper we investigate conditions under which there exists a pair (X,x*) such that Δ₀(X, x*) is isomorphic to a given preordered set.

2000 Mathematics Subject Classification.   54F20, 54F50, 05C20.

Key words and phrases.   Dendroid, preordered set, partially ordered set.