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I would only remark that these are statements more about the manner in which
we have chosen to partition the area of a sphere rather than about the
intrinsic topological properties of a sphere. I think that the only
intrinsic topological content of these “equator –based” statements is simply
that a great circle (any great circle) is larger (in radius and
circumference) than any other circle drawn on the surface of a 3-sphere.