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Regularity of $ R(X)$ does not pass to finite unions


Author: J. F. Feinstein
Journal: Proc. Amer. Math. Soc. 148 (2020), 2931-2936
MSC (2010): Primary 46J10
DOI: https://doi.org/10.1090/proc/14944
Published electronically: March 18, 2020
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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.


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Additional Information

J. F. Feinstein
Affiliation: University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
Email: Joel.Feinstein@nottingham.ac.uk

DOI: https://doi.org/10.1090/proc/14944
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
Article copyright: © Copyright 2020 American Mathematical Society