Finite Approximate Selections Of Certain Light Open And Closed Mappings
by
Louis F. McAuley
Binghamton University

Suppose that U is an open connected subset of Rⁿ such that [`U] is a Peano continuum. Certain light open and closed mappings \phi:[`U] --> Y (a metric space). Given \epsilon > 0, there is a set valued map F:Y --> Rⁿ such that F(y) is finite for each y in Y, N_\epsilon(\phi^-1\phi(x)) contains F(\phi(x)), and F is continuous in the sense that if {y_i} --> y, then {F(y_i)} --> F(y). There are conditions under which F can be replaced by a continuous (single valued) map f such that f\phi is homotopic to the identity without moving \partialU across the origin o in U.

Date received: February 4, 1998