Weakly chainable circle-like continua

This paper investigates the problem of ascertaining which circle-like continue are continuous images of chainable continue. In the second chapter, the notion of the "revolving number" of a map from S[raised 1] onto S[raised 1] is introduced and used to classify the planar, non-chainable, circle-like continua by structure: decomposable; "self-entwined" (a notion introduced in chapter 2); indecomposable, non-self-entwined. The main theorem in chapter 3 is a characterization of weakly chainable circle-like continua; the classification scheme of chapter 2 is used to prove this result.