On a question concerning sharp bases

A sharp base B is a base such that whenever ( B i ) i < ω is an injective sequence from B with x ∈ ⋂ i < ω B i , then { ⋂ i < n B i : n < ω } is a base at x. Alleche, Arhangel'skiĭ and Calbrix asked: if X has a sharp base, must X × [ 0 , 1 ] have a sharp base? Good, Knight and Moham...

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Bibliographic Details
Published inTopology and its applications Vol. 153; no. 1; pp. 90 - 96
Main Authors Bailey, Bradley, Gruenhage, Gary
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2005
Subjects
Pseudocompact
Sharp base
54D70
Pseudocompact
Sharp base
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Summary:A sharp base B is a base such that whenever ( B i ) i < ω is an injective sequence from B with x ∈ ⋂ i < ω B i , then { ⋂ i < n B i : n < ω } is a base at x. Alleche, Arhangel'skiĭ and Calbrix asked: if X has a sharp base, must X × [ 0 , 1 ] have a sharp base? Good, Knight and Mohamad claimed to construct an example of a Tychonoff space P with a sharp base such that P × [ 0 , 1 ] does not have a sharp base. However, the space was not regular. We show how to modify the construction to make P Tychonoff.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2004.02.021