For a double cover whose projection admits no continuous section,
we take two copies of the upper half-plane, topologized by ...
taking as basic open neighborhoods of points on either x-axis
the symmetric “broken open Vs”, with fingers of equal length,
but with left finger in the same half-plane as the point on the x-axis,
and right finger in the other half-plane (omitting the corresponding point on
that other x-axis).
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