In this note certain
one-dimensional continua are defined for finite 2-complexes. These continua, called
S-curves, are a generalization of the Sierpinski plane universal curve. By a 2-complex
is meant a finite connected 2-dimensional euclidean polyhedron which has a
triangulation such that every l-simplex is the face of at least one 2-simplex. It is
shown that any two S-curves in a 2-complex are homeomorphic. In addition, it is
established that two 2-complexes (with the property that every l-simplex in a
triangulation is the face of two or more 2-simplexes) are homeomorphic if and only if
the corresponding S-curves are homeomorphic.
