Thus there are at most countably many points along the lower edge of Heath’s
V-space, having
neighborhoods on which the section f
is defined and continuous,
and so this covering has no continuous global section.
Of interest to topos theorists, because it shows that supports need not split
(“(SS) fails”) even in a topos where
(SG) Subobjects of 1 Generate, and
(IC) “Internal Choice” holds (i.e., epimorphisms split locally).