Light Open and Open Mappings on Manifolds. II
John J. Walsh · Transactions of the American Mathematical Society · 1976
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.