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On weakly flat $ 1$-spheres


Author: Robert J. Daverman
Journal: Proc. Amer. Math. Soc. 38 (1973), 207-210
MSC: Primary 57A40; Secondary 57A45
DOI: https://doi.org/10.1090/S0002-9939-1973-0310894-X
MathSciNet review: 0310894
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Abstract: With his cellularity criterion, McMillan has provided a characterization of those complementary domains of an $ (n - 1)$-sphere in the $ n$-sphere $ {S^n}$ that are open $ n$-cells $ (n \ne 4)$. Paul F. Duvall has used the cellularity criterion to characterize those $ k$-spheres $ \Sigma $ in $ {S^n}(2 \leqq k \leqq n - 3)$ such that $ {S^n} - \Sigma $ is homeomorphic to the complement of the standard $ k$-sphere in $ {S^n}$. The purpose of this note is to indicate how McMillan's methods can be reapplied to handle the case $ k = 1(n \ne 4)$ as well.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310894-X
Keywords: Weakly flat, global $ 1$-alg property, cellularity criterion, radial engulfing, spine of a regular neighborhood, degree one mapping
Article copyright: © Copyright 1973 American Mathematical Society

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