## Failure of rational approximation on some Cantor type sets

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- by Albert Mas-Blesa
- Proc. Amer. Math. Soc.
**137**(2009), 635-640 - DOI: https://doi.org/10.1090/S0002-9939-08-09573-7
- Published electronically: June 20, 2008
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## Abstract:

Let $A(K)$ be the algebra of continuous functions on a compact set $K\subset \mathbb {C}$ which are analytic on the interior of $K$, and let $R(K)$ be the closure (with respect to uniform convergence on $K$) of the functions that are analytic on a neighborhood of $K$. A counterexample of a question posed by A. O’Farrell about the equality of the algebras $R(K)$ and $A(K)$ when $K=(K_{1}\times [0,1])\cup ([0,1]\times K_{2})\subseteq \mathbb {C}$, with $K_{1}$ and $K_{2}$ compact subsets of $[0,1]$, is given. Also, the equality is proved with the assumption that $K_{1}$ has no interior.## References

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## Bibliographic Information

**Albert Mas-Blesa**- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
- Email: amblesa@mat.uab.cat
- Received by editor(s): February 6, 2008
- Published electronically: June 20, 2008
- Additional Notes: This work was supported by grant AP2006-02416 (Programa FPU del MEC, España), and also partially supported by grants 2005SGR-007749 (Generalitat de Catalunya) and MTM2007-62817 (MEC, España)
- Communicated by: Mario Bonk
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 635-640 - MSC (2000): Primary 30C85; Secondary 31A15
- DOI: https://doi.org/10.1090/S0002-9939-08-09573-7
- MathSciNet review: 2448585