Mapping cylinder neighborhoods in the plane
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- by Beverly Brechner and Morton Brown
- Proc. Amer. Math. Soc. 84 (1982), 433-436
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640248-3
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Abstract:
We characterize those compact subsets of the plane which have mapping cylinder neighborhoods, describe the neighborhood closures, and show that such neighborhood closures are topologically unique. The proofs employ the notion of prime ends. We also show that if $U$ is a mapping cylinder neighborhood of a pointlike continuum in ${S^3}$, then $\overline U$ is a $3$-cell.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 433-436
- MSC: Primary 57N05; Secondary 54F25, 57N60
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640248-3
- MathSciNet review: 640248