# Metrics for modelling convergence in the lambda-calculus

I wonder if there have been efforts to reconcile the measure approach to termination and Scott's domain theory or other topological models of computation. In other words, can we translate this measure that one use in automation of program termination to metric or measures in a topological interpretation of a programming language?

Examples:

$$\Omega = (\lambda x. x x) (\lambda x. x x)$$

References:

Models and theories of lambda calculus

Computable topology

• @AndrejBauer thank you for your suggestion. To clarify, by "open property" you mean something for which we don't have an answer? – Rodrigo Nov 13 '19 at 12:35