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Figure Captions

Figure 1a. Diagonal Black and White holes in the two
dimensional ω-plane. Only two direct paths can link points
a and b which are continuously deformable into one another
without crossing either hole. There are two additional mono-
tonic switchback paths which are not drawn.

Figure 1b. Cross-diagonal Black and White holes as in 1a.
Three direct equivalence classes of continuously deformable
paths can link a and b. Thus the two spaces are topologi-
cally distinct. Here monotonic switchbacks are not possible,
although relaxation of that condition can lead to ‘backwards’
switchbacks and intermediate loopings.

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