**Makkai workship Birthday offering**

Billed to the organisers as “a short talk ... offering
a peculiar
topological space that Peter Johnstone and I used some 30 years ago
to solve a topoidal problem.”

The space? — Heath’s *V*-space, a re-topologised real
upper half-plane. (Actually: the quotient space of
**R**_{discrete} × **R**_{metric}
under the equivalence relation
(*x*-*y*, *y*) ~ (*x*+*y*, -*y*) ,
the metric on the second factor being given
by: *d*(*x*, *y*)
= (1-δ_{x,y})·*max*{|*x*|, |*y*|}
.)
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