A duality between spheres and spheres with arcs
Author:
Carl D. Sikkema
Journal:
Proc. Amer. Math. Soc. 25 (1970), 781-785
MSC:
Primary 54.78
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259877-6
MathSciNet review:
0259877
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Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this paper is to extend the authors duality between nearly tame spheres and nearly tame arcs to a duality between wild spheres and tame spheres with nearly tame arcs properly attached, one arc for each wild point of the wild sphere.
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- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979β990. MR 27512, DOI https://doi.org/10.2307/1969408 N. Hosay, The sum of a cube and a crumpled cube is ${S^3}$, Abstract #607-17, Notices Amer. Math. Soc. 10 (1963), 666.
- Lloyd L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534β549. MR 178460, DOI https://doi.org/10.1090/S0002-9947-1965-0178460-7
- Joseph Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147β151. MR 190914
- Carl D. Sikkema, A duality between certain spheres and arcs in $S^{3}$, Trans. Amer. Math. Soc. 122 (1966), 399β415. MR 199851, DOI https://doi.org/10.1090/S0002-9947-1966-0199851-5
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Additional Information
Keywords:
Arc,
<IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$2$">-sphere,
<IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$3$">-sphere,
duality,
tame,
wild,
locally flat,
upper semicontinuous decomposition
Article copyright:
© Copyright 1970
American Mathematical Society