# Definition:Scott Topology

## Definition

Let $\struct {S, \preceq}$ be an up-complete ordered set.

Let $T = \struct {S, \preceq, \tau}$ be a relational structure with topology.

Then $T$ has the Scott topology if and only if:

$\tau$ is the set of all upper and inaccessible by directed suprema subsets of $S$.

## Also see

• Results about the Scott topology can be found here.

## Source of Name

This entry was named for Dana Stewart Scott.