...the relation of betweenness on the torus is undetermined for curves that cannot be contracted to a point [e. g., circles around a doughnut hole], i. e., for three of such curves it is not uniquely determined which of them lies between the other two... This indeterminateness... has the consequence that such a curve [alone] does not divide the surface of the torus into two separate domains; between points to the "right" and to the "left" of the line. (Hans Reichenbach)

...the relation of betweenness on the torus is undetermined for curves that cannot be contracted to a point [e. g., circles around a doughnut hole], i. e., for three of such curves it is not uniquely determined which of them lies between the other two... This indeterminateness... has the consequence that such a curve [alone] does not divide the surface of the torus into two separate domains; between points to the "right" and to the "left" of the line.

Hans Reichenbach

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curve divide doughnut hole left line point right surface three torus lies points

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