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An almost continuous function ๐‘“: ๐‘†โฟโ†’๐‘†^{๐‘š} which commutes with the antipodal map

An almost continuous function ๐‘“: ๐‘†โฟโ†’๐‘†^{๐‘š} which commutes with the antipodal map

It is shown that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n comma m greater-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>โฉพ<!-- โฉพ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n,m \geqslant 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are integers, then there exists an almost continuous function from the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation โ€ฆ