Continuum-wise injective maps

摘要

We prove that for each n >= 1 the set of all surjective continuum-wise injective maps from an n-dimensional continuum onto an LCn-1-continuum with the disjoint (n-1, n)-cells property is a dense G(delta)-subset of the space of all surjective maps. As a corollary, we get the following result which is essentially proved. in [5]; the set of all arcwise increasing maps from the closed unit interval onto a Peano continuum without free arcs is a dense Gs-subset of the space of all surjective maps. (C) 2016 Elsevier B.V. All rights reserved.