# Definition:Scott Topology

## Definition

Let $T = \left({S, \preceq, \tau}\right)$ be a relational structure with topology

where $\left({S, \preceq}\right)$ is an up-complete ordered set.

Then $T$ has Scott topology if and only if

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

## Source of Name

This entry was named for Dana Stewart Scott.