The continuity of Darboux injections between manifolds

Iryna Banakh,Taras Banakh

doi:10.1016/j.topol.2019.107031

The continuity of Darboux injections between manifolds

Iryna Banakh, Taras Banakh

Open Access

https://doi.org/10.1016/j.topol.2019.107031

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Journal: Topology and its Applications	Publication Date: Dec 13, 2019
Citations: 7	License type: publisher-specific-oa

Affiliation: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Jan Kochanowski University, Lviv University

#Homology 3-sphere #Injective Map + Show 3 more

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Abstract

We prove that an injective map f:X→Y between metrizable spaces X,Y is continuous if for every connected subset C⊂X the image f(C) is connected and one of the following conditions is satisfied:•Y is a 1-manifold and X is compact and connected;•Y is a 2-manifold and X is a closed 2-manifold;•Y is a 3-manifold and X is a rational homology 3-sphere. This gives a partial answer to a problem of Willie Wong, posed on Mathoverflow.

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