Definition:Scott Topology
Jump to navigation
Jump to search
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.
Sources
- 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices
- Mizar article WAYBEL11:def 4