Abstract:A pseudocone over $X$ is a compactification of $(0, 1]$ with remainder $X$. $S$ is a circle. A characterization of those pseudocones over $S$ which are weakly chainable is given. (A continuum is weakly chainable if and only if it is a continuous image of the pseudoarc.) Covering projections and liftings are used, and a simple geometric interpretation of the result is that a pseudocone over $S$ is weakly chainable if and only if the absolute value of the winding number of any subarc of $(0, 1]$ around $S$ is bounded by some $m > 0$.
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- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 476-478
- MSC: Primary 54F20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0365515-9
- MathSciNet review: 0365515