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

J. F. Feinstein
2019 Proceedings of the American Mathematical Society  

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2019 pre-print arXiv:1912.02602v1 fatcat:hhj5ha3iivgirhpeynnrrp52my
We show that there are compact plane sets X, Y such that R(X) and R(Y) are regular but R(X ∪ Y) is not regular.
doi:10.1090/proc/14944 fatcat:kszn54wchfaifabzapzoyxps3i
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J. F. Feinstein. "Regularity of $R(X)$ does not pass to finite unions." Proceedings of the American Mathematical Society 148.7 (2019)