A note on primitive skew curves

By a primitive skew curve of type I we mean any topological image of the complex C which consists of two groups of three vertices each and nine 1-cells, in a fashion that each vertex of one group together with each vertex of the other group bounds a 1-cell. By a primitive skew curve of type II we mean any topological image of the complex D which consists of five vertices and ten 1-cells in a fashion that each pair of vertices bounds a 1-cell. In 1934 Claytor proved that every cyclic locally connected continuum containing no primitive skew curve of either type must be homeomorphic with a subset of a spherical surface. In this note we point out that for a large class of locally connected continua the property of being planar may be insured merely by requiring that the given locally connected continuum contain no primitive skew curve of type I. Stated precisely, our principal theorem is the following: