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Light open and open mappings on manifolds. II


Author: John J. Walsh
Journal: Trans. Amer. Math. Soc. 217 (1976), 271-284
MSC: Primary 57A15; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9947-1976-0394674-2
MathSciNet review: 0394674
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Abstract: Sufficient conditions are given for the existence of light open mappings between p.l. manifolds. In addition, it is shown that a mapping f from a p.l. manifold $ {M^m},m \geqslant 3$, to a polyhedron Q is homotopic to an open mapping of M onto Q iff the index of $ {f_\ast}({\pi _1}(M))$ in $ {\pi _1}(Q)$ is finite. Finally, it is shown that an open mapping of $ {M^m}$ onto a p.l. manifold $ {N^n},n \geqslant m \geqslant 3$, can be approximated by a light open mapping of M onto N.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0394674-2
Keywords: Light open mapping, open mapping, p.l. manifold, polyhedron
Article copyright: © Copyright 1976 American Mathematical Society

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