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

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.

7 pages, no figures, to appear in Proc. AMS

References in corpus (1)

• Partial regularity and t-analytic sets for Banach function algebras