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A two-color theorem for analytic maps in ๐‘…โฟ

A two-color theorem for analytic maps in ๐‘…โฟ

<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f 1 comma midline-horizontal-ellipsis comma f Subscript k Baseline"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mo>,</mml:mo> <mml:mo>โ‹ฏ<!-- โ‹ฏ --></mml:mo> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">{f_1}, \cdots ,{f_k}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are real analytic functions on <inline-formula content-type="math/mathml"> <mml:math โ€ฆ