Continuum-wise injective maps

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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 [5]; 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.

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