Regularity of $R(X)$ does not pass to finite unions
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Abstract:
We show that there are compact plane sets $X$, $Y$ such that $R(X)$ and $R(Y)$ are regular but $R(X \cup Y)$ is not regular.References
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Additional Information
- J. F. Feinstein
- Affiliation: University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- MR Author ID: 288617
- Email: Joel.Feinstein@nottingham.ac.uk
- Received by editor(s): April 8, 2019
- Received by editor(s) in revised form: July 30, 2019, and November 11, 2019
- Published electronically: March 18, 2020
- Communicated by: Stephen Dilworth
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2931-2936
- MSC (2010): Primary 46J10
- DOI: https://doi.org/10.1090/proc/14944
- MathSciNet review: 4099781