Abstract
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 Gδ-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 Gδ-subset of the space of all surjective maps.
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