NMSU • BLAST-2009
Something Old, Something New, Something Borrowed, ...
Next F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus

  Billed to the organisers as “a short talk about a peculiar topological space that Peter Johnstone, Bob Paré and I used some 30 years ago to solve a topoidal problem.”
The space?Heath’s V-space (a suitably re-topologised real upper half-plane).
In detail:The quotient space of Rdiscrete × Rmetric under the equivalence relation (x-y, y) ~ (x+y, -y) , the metric on the second factor being given by  d(x, y) = (1-δx,y)·max{|x|, |y|} .
The double cover?Concocted by emulating one construction of the connected double cover of the circle.
The motivation?To display a topos — that of locally finite (i.e., decidable and Kuratowski-finite) sheaves over Heath’s V-space — where subobjects of 1 generate and internal choice holds ((SG) & (IC)), yet supports do not split ((SS) fails, and with it, (AC)).