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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Isotoping mappings to open mappings


Author: John J. Walsh
Journal: Trans. Amer. Math. Soc. 250 (1979), 121-145
MSC: Primary 57N37; Secondary 54C10, 57N25, 57N60
MathSciNet review: 530046
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Abstract: Let f be a quasi-monotone mapping from a compact, connected manifold $ {M^m}\,(m\, \geqslant \,3)$ onto a space Y; then there is an open mapping g from M onto Y such that, for each $ y\, \in \,Y,\,{g^{ - 1}}(y)$ is not a point and $ {g^{ - 1}}(y)$ and $ {f^{ - 1}}(y)$ are equivalently embedded in M (in particular, $ {g^{ - 1}}(y)$ and $ {f^{ - 1}}(y)$ have the same shape). Applying the result with f equal to the identity mapping on M yields a continuous decomposition of M into cellular sets each of which is not a point.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0530046-8
PII: S 0002-9947(1979)0530046-8
Keywords: Open mapping, monotone mapping, manifold, cellular
Article copyright: © Copyright 1979 American Mathematical Society