Limit properties of induced mappings

Abstract

Given a class M of mappings f between continua, near-M stands for the class of uniform limits of sequences of mappings from M. Let 2 f and C(f) mean the induced mappings between hyperspaces. Relations are studied between the conditions: f ∈ near-M, 2 f ∈ near-M and C(f) ∈ near-M. A special attention is paid to the classes M of open and of monotone mappings.