Continuum-wise injective maps

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 essential...

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Bibliographic Details
Published in:Topology and its applications 2016-04, Vol.202, p.410-417
Main Authors: Kato, Hisao, Matsuhashi, Eiichi
Format: Article
Language:English
Subjects:
Continuum-wise injective map
Disjoint [formula omitted]-cells property
Hereditarily irreducible map
Locally connected in dimension n
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Summary: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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2016.01.029