The notion of rectilinear k-simplex appears in Theorem 10.27 of Rudin's book "Principles of Mathematical analysis", then what is the definition of a rectilinear k-simplex? I read the proof of Theorem 10.27 and think that the proof treats oriented affine k-simplex instead of rectilinear k-simplex, is it right?
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Yeah, I understand it the same way. Since Rudin refers back to equation (75), the definition of "oriented affine k-simplex", I believe he means "oriented affine k-simplex" by "oriented rectilinear k-simplex".
Henry
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@Leucippus Why is it not an answer? The OP suspects that Rudin should use the word "affine" instead of "rectilinear", the latter not being defined in the book. The OP is right and the answer confirms it. – Paul Frost Jul 08 '19 at 23:35