Functional countability in GO spaces

We prove that, for any GO space X, if ext(X)≤ω and X is either scattered or locally countable, then X is functionally countable. Every functionally countable GO space X has countable extent and |A‾|≤ω for any countable set A⊂X. It is also shown that functional countability of every ω-scattered GO sp...

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Bibliographic Details
Published in:Topology and its applications 2022-10, Vol.320, p.108233, Article 108233
Main Authors: Tkachuk, V.V., Wilson, R.G.
Format: Article
Language:English
Subjects:
Extent
Functionally countable space
GO space
Lindelöf space
Linearly ordered space
Locally countable space
Scattered space
Weak Borel hypothesis
ω-scattered space
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Summary:We prove that, for any GO space X, if ext(X)≤ω and X is either scattered or locally countable, then X is functionally countable. Every functionally countable GO space X has countable extent and |A‾|≤ω for any countable set A⊂X. It is also shown that functional countability of every ω-scattered GO space of countable extent is equivalent to Weak Borel Hypothesis.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108233