A $2$-sphere of vetical order $5$ bounds a $3$-cell
Author:
L. D. Loveland
Journal:
Proc. Amer. Math. Soc. 26 (1970), 674-678
MSC:
Primary 54.78
DOI:
https://doi.org/10.1090/S0002-9939-1970-0268871-0
MathSciNet review:
0268871
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Abstract | References | Similar Articles | Additional Information
Abstract: A subset $X$ of ${E^3}$ is said to have vertical order $n$ if no vertical line contains more than $n$ points of $X$. We prove that each $2$-sphere in ${E^3}$ which has vertical order 5 bounds a $3$-cell.
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Additional Information
Keywords:
Tame <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$2$">-spheres,
tame surfaces,
embeddings in <IMG WIDTH="31" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${E^3}$">,
surfaces in <IMG WIDTH="31" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img19.gif" ALT="${E^3}$">,
<IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\ast$">-taming sets,
vertical order
Article copyright:
© Copyright 1970
American Mathematical Society