Antipodal coincidence for maps of spheres into complexes
Antipodal coincidence for maps of spheres into complexes
This paper gives a partial answer to the question of whether there exists a Borsuk-Ulam type theorem for maps of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{S^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into lower-dimensional spaces, which are not necessarily manifolds. It …