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

contradictory requirements on the section   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).
  In particular, epimorphisms need not actually split, i.e., (AC) may fail, i.e., the well-known implication (AC) ⇒ (IC) & (SG) is not reversible.
  The topos: that of locally finite sheaves over Heath’s V-space.