A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem

Details A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem

2011-04-05

arxiv.org/abs/1104.0833v1

Mathematics

Complex Variables

Scientific paper

We investigate the set of uniform limits of polynomials on any closed Jordan domain with respect to the chordal metric $\chi$ on $\mathbb{C}\cup\{\infty \}$. We conclude that Mergelyan's Theorem may be extended to the case of uniform approximation with respect to $\chi$ on closed Jordan domains. Similar results are obtained if we replace the one point compactification $\mathbb{C}\cup\{\infty\}$ of $\mathbb{C}$ by another compactification of $\mathbb{C}$ homeomorphic to the closed unit disc.

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