||Continuum-wise injective maps
Kato, HisaoMatsuhashi, Eiichi
Topology and its applications
417 , 2016-04 , Elsevier
We prove that for each n≥1n≥1 the set of all surjective continuum-wise injective maps from an n -dimensional continuum onto an LCn−1LCn−1-continuum with the disjoint (n−1,nn−1,n)-cells property is a dense GδGδ-subset of the space of all surjective maps. As a corollary, we get the following result which is essentially proved in ; the set of all arcwise increasing maps from the closed unit interval onto a Peano continuum without free arcs is a dense GδGδ-subset of the space of all surjective maps.