Light open and open mappings on manifolds. II

Walsh, John J.

doi:10.1090/S0002-9947-1976-0394674-2

Light open and open mappings on manifolds. II
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Trans. Amer. Math. Soc. 217 (1976), 271-284 Request permission

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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