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A continuity theorem for Fuchsian groups

A continuity theorem for Fuchsian groups

On a given Riemann surface, fix a discrete (finite or infinite) sequence of points <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace upper P Subscript k Baseline right-brace comma k equals 1 comma 2 comma 3 comma ellipsis comma"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mo fence="false" …