A fiberable continuum which is not nontrivially productable

We construct a continuum X⊆R3 such that there exists a continuous surjection f from X onto X with the inverse image of every point being of the same size as the continuum and such that for no topological space T whose every point has a nontrivial neighbourhood there exists a surjection from X onto X...

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Bibliographic Details
Published in:	Topology and its applications Vol. 304; p. 107789
Main Authors:	Cichoń, Jacek, Morayne, Michał, Rałowski, Robert
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-12-2021
Subjects:	Fiberable space Inverse images Product spaces Productable space Surjection Fiberable space 54F15 54C05 Inverse images Productable space Product spaces Surjection
Online Access:	Get full text
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Summary:	We construct a continuum X⊆R3 such that there exists a continuous surjection f from X onto X with the inverse image of every point being of the same size as the continuum and such that for no topological space T whose every point has a nontrivial neighbourhood there exists a surjection from X onto X×T. In particular, f cannot be a composition of a surjection from X onto X×T and the projection onto X, where T is of the same size as the continuum and satisfies the above neighbourhood condition.
ISSN:	0166-8641 1879-3207
DOI:	10.1016/j.topol.2021.107789