# nLab Scott topology

The Scott topology on a preorder is the topology in which the open sets are those whose characteristic functions (from the given preorder into the preorder of truth values) preserve directed joins (and this makes the characteristic function necessarily monotonic). This in fact ensures that, in general, the continuous functions between preorders with the Scott topologies are precisely those (necessarily monotonic) functions between them which preserve directed joins. (The preorder of truth values itself, therefore, when equipped with the Scott topology, becomes the open set classifier, Sierpinski space.)

Revised on January 30, 2013 08:05:15 by Anonymous Coward (181.1.209.2)