Vol. 50, No. 1, 1974

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Sierpinski curves in finite 2-complexes

Gail Atneosen

Vol. 50 (1974), No. 1, 1–5

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.

Mathematical Subject Classification 2000
Primary: 54F50
Received: 12 June 1972
Revised: 16 October 1972
Published: 1 January 1974
Gail Atneosen