Noninvariance of an approximation property for closed subsets of Riemann surfaces
Noninvariance of an approximation property for closed subsets of Riemann surfaces
A closed subset <italic>E</italic> of an open Riemann surface <italic>M</italic> is said to have the approximation property <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script a"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">a</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if each continuous function on <italic>E</italic> which is analytic at all interior points of …