A fiberable continuum which is not nontrivially productable II

We construct a metric continuum X such that there exists a continuous surjection F from X onto X with the inverse image of every point of size of the continuum and such that for no nontrivial topological space T there exists a surjection from X onto X×T. In particular, F cannot be a composition of a...

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Bibliographic Details
Published in:Topology and its applications 2021-10, Vol.302, p.107830, Article 107830
Main Authors: Cichoń, Jacek, Morayne, Michał, Rałowski, Robert
Format: Article
Language:English
Subjects:
Fiberable space
Inverse images
Product spaces
Productable space
Surjection
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Summary:We construct a metric continuum X such that there exists a continuous surjection F from X onto X with the inverse image of every point of size of the continuum and such that for no nontrivial topological space T 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 a topological space of size of the continuum with at least one nonempty open set not equal to the whole space. This is a sharpening of the result obtained in [2].
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2021.107830