Scott continuity

The Scott topology, named after Dana Scott, is a topology that results from the partial order on a semi- minor amounts. It plays a role in theoretical computer science, among others.

Definition

It should be a lot with partial order. A subset is called Scott -closed if

• With respect to a sub- half amount, that is, with each item also each with respect to the partial order contains smaller, and
• For all statements, which have a supremum is.

The so defined Scott - closed sets are exactly the quantities of the Scott topology concluded.

Properties

Below are and partially ordered sets, and they are equipped with the respective Scott topology.

• Is a continuous map, so is monotonic.
• A picture is continuous if directed Suprema receives, ie is looking for all with supremum.