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SUMMARY:Remarks on punctual local connectedness - Prof. Peter Johnstone\, 
 DPMMS
DTSTART:20091027T141500Z
DTEND:20091027T154500Z
UID:TALK20993@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:We study the condition\, on a connected and locally connected 
 geometric morphism $p:{\\cal E}\\to{\\cal S}$\, that the canonical natural
  transformation $p_*\\to p_!$ should be (pointwise) epimorphic --- a condi
 tion which F.W. Lawvere called the `Nullstellensatz'\, but which we prefer
  to call `punctual local connectedness'. We show that this condition impli
 es that $p_!$ preserves finite products\, and that\, for bounded morphisms
  between toposes with natural number objects\, it is equivalent to being b
 oth local and hyperconnected. 
LOCATION:MR9\, Centre for Mathematical Sciences
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