Prof. Dana Scott gave a few talks on Lambda Calculus, and some of them are available on Youtube.

Once you define Topology, you may define continuous functions

A list of them can be found here:

Local Links
Video/Dana S. Scott Lambda Calculus, Then and Now
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 1) - λC 2018
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 2) - λC 2018
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 3) - λC 2018
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 4) - λC 2018
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 5) - λC 2018
Video/Dana Scott & Jeremy Siek - Theory & Models of Lambda Calculus: Typed and Untyped (Part 6) - λC 2018
Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 1 of 5 - λC 2017
Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 2 of 5 - λC 2017
Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5 - λC 2017
Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 4 of 5 - λC 2017
Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 5 of 5 - λC 2017
Video/Stochastic Lambda-Calculus

Dana Scott on Lambda Calculus