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An $\omega _{2}$-minimal Boolean algebra


Author: Mariusz Rabus
Journal: Trans. Amer. Math. Soc. 348 (1996), 3235-3244
MSC (1991): Primary 03E35; Secondary 06E15, 54D80
DOI: https://doi.org/10.1090/S0002-9947-96-01663-7
MathSciNet review: 1357881
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Abstract: For every linear order $L$ we define a notion of $L$-minimal Boolean algebra and then give a consistent example of an $\omega _{2}$-minimal algebra. The Stone space $X$ of our algebra contains a point $\{*\}$ such that $X-\{*\}$ is an example of a countably tight, initially $\aleph _{1}$-compact, non-compact space. This answers a question of Dow and van Douwen.


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Additional Information

Mariusz Rabus
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
Email: rabus@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9947-96-01663-7
Received by editor(s): January 17, 1995
Received by editor(s) in revised form: October 27, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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