13 Mar
1991
13 Mar
'91
5:11 p.m.
Given a locale A, one may endow the set of points Loc(1,A) with the relative topology enherited from A, (and thereby produce the "spatial part of A"). Or, viewing Loc(1,A) as a poset with directed sups (in the "specialization" ordering), one may equip Loc(1,A) with the Scott topology. I have convinced myself that for arbitrary A, the Scott topology is at least as fine as the relative topology. Are there conditions on the locale A which characterize the coincidence of these two ways one might topologize its set of points? Paul