1 Jan 15:59 2011

### Does this topology have a name?

Michael Barr <barr <at> math.mcgill.ca>

2011-01-01 14:59:48 GMT

2011-01-01 14:59:48 GMT

Let A be a model of a finitary equational theory and let X be the set of congruences on A. For a,b in A, let M(a,b) = {E} such that E is a congruence on A and aEb. Does this topology have a name? It turns out that this topology is coherent which means, among other things, that if we make the M(a,b) clopen, the result is a Stone space. Obviously in a ring, we could instead use the set of ideals, but aside from the fact that that will include non-prime ideals, the topology is the opposite of the Zariski topology. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]