2022-01-262022-01-26197413705127https://hdl.handle.net/10657/8578This 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.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital