## Monotone and open mappings on manifolds. I

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- by John J. Walsh
- Trans. Amer. Math. Soc.
**209**(1975), 419-432 - DOI: https://doi.org/10.1090/S0002-9947-1975-0375326-0
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## Abstract:

Sufficient conditions are given for the existence of open mappings from a p. 1. manifold ${M^m},m \geqslant 3$, onto a polyhedron $Q$. In addition, it is shown that a mapping $f$ from ${M^m},m \geqslant 3$, to $Q$ is homotopic to a monotone mapping of $M$ onto $Q$ iff ${f_ \ast }:{\pi _1}(M) \to {\pi _1}(Q)$ is onto. Finally, it is shown that a monotone mapping of ${M^m},m \geqslant 3$, onto $Q$ can be approximated by a monotone open mapping of $M$ onto $Q$.## References

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## Bibliographic Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**209**(1975), 419-432 - MSC: Primary 57A15; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0375326-0
- MathSciNet review: 0375326