We will discuss the proof of this fact, which involves dominant functions, in the hopes that it will lead us toward proving in the future new domination arguments arising in connection with the recent results relating computability to differential geometry. Thursday, Nov. 16, 2000. We will present a framework for computable topology based on recent developments that began in 1996 with Dana Scott's equilogical spaces. This setup can then be extended to equilogical spaces by equipping the topological spaces with equivalence relations. The benefit of adding the equivalence relations is that they let us distinguish between the points of a space and the names of points, similar to the distinction between r.e. sets and Goedel codes of r.e. sets.
Equilogical spaces form a category that has very good closure properties.
For example, it is cartesian closed, which means that we can form all function spaces, function spaces of function spaces, etc. This cannot be done if we restrict attention only to topological spaces. In the last part of the talk we will show how computability on real numbers and real functions is treated in equilogical spaces.