#Reading through Dyson's 1951 paper "Continuous Functions Defined on Spheres"

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meager pasture
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Attached is a screenshot of Lemma 1. My question is, what could be a practical example of such a set of points A? Couldn't you always be able to draw a continuous arc in a "parallel" direction to the plane? Or does this not count as we only consider points within the plane?

autumn flameBOT