Weak chainability of pseudocones

Bellamy, David P.

doi:10.1090/S0002-9939-1975-0365515-9

Weak chainability of pseudocones
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by David P. Bellamy PDF

Proc. Amer. Math. Soc. 48 (1975), 476-478 Request permission

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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Topological properties of compactifications of a half open interval

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