An isolated bounded point derivation

O’Farrell, Anthony G.

doi:10.1090/S0002-9939-1973-0315452-9

An isolated bounded point derivation
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by Anthony G. O’Farrell PDF

Proc. Amer. Math. Soc. 39 (1973), 559-562 Request permission

Abstract:

For a compact subset $X$ of the plane, $R(X)$ denotes the class of uniform limits on $X$ of rational functions with poles off $X$. $R(X)$ is a function algebra on $X$. An example $X$ is constructed such that $R(X)$ admits a bounded point derivation at exactly one point of $X$.

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