某些Cantor型集上有理逼近的失效
Failure of rational approximation on some Cantor type sets
摘要：
设$A(K)$是紧集$K\subset\mathbb C$上在$K$内部解析的连续函数的代数，$R(K)$是在$K$邻域上解析的函数的闭包（在$K$上一致收敛）.对A. O 'Farrell关于代数$R(K)$和$A(K)$的等价性，当给出$K=(K_{1}\times[0,1])\cup([0,1]\times K_{2})\subseteq\mathbb C$，有$[0,1]$的紧子集$K_{1}$和$K_{2}$时.在假设$K_{1}$无内部的条件下，证明了等式的成立.
英文摘要：
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 $R(K)$ the closure (with the uniform convergence on $K$) of the functions that are analytic on a neighborhood of $K$. A counterexample of a question made 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
