Scott's graph model is a model of the untyped -calculus. It was discovered by Dana Scott in the mid-1970s, and presented in the landmark paper [Scott 1976].
The carrier of the model is the set
of subsets of natural numbers (where we use the ordinal notation to stand for natural numbers).
The graph model has strong connections with both the notion of continuity from domain theory, but also various notions from computability theory.
Let be the Sierpiński space, with the usual topology. Then the graph model is homeomorphic to its infinite product:
See [Scott 1976, Appendix A].
Scott, Dana S. 1976. ‘Data Types as Lattices’. SIAM Journal on Computing 5 (3): 522–87. https://doi.org/10.1137/0205037.
@article{scott_1976,
title = {Data {Types} as {Lattices}},
volume = {5},
doi = {10.1137/0205037},
number = {3},
journal = {SIAM Journal on Computing},
author = {Scott, Dana S.},
year = {1976},
pages = {522--587},
file = {Attachment:C\:\\Users\\tz20861\\Zotero\\storage\\CM9NV7SM\\Scott - 1976 - Data Types as Lattices.pdf:application/pdf},
}