9 Sep
2011
9 Sep
'11
11:11 a.m.
On Wed, 7 Sep 2011, Vasili I. Galchin wrote:
In which paper did Lawvere and Tierney lay out the relationship between these two topologies?
I don't know where the proof of the equivalence was first written down. But it was stated clearly by Lawvere in his Introduction to Springer LNM 274 (1972): "At the Rome and Overwolfach [sic] meetings I had pointed out that the usual notion of a Grothendieck topology is equivalent to a single such morphism j [that is, a Lawvere-Tierney topology]; Tierney showed that the appropriate axioms on j are simply that jj = j and j preserves finite conjunctions." Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]