# Thread: Topological Space, Continuous, G delta

1. ## Topological Space, Continuous, G delta

Let X and Y be topological spaces, and let f:X->Y. Let C denote the set of points at which f is continuous. What axioms (of separation) must X and/or Y satisfy such that C is a G delta set?

2. ## Re: Topological Space, Continuous, G delta

The fact that the discontinuity set of a function from R to R with its usually topology is a F-sigma set is one of the most succinct proofs that such a function cannot have the rationals equivalent to its continuity set. As R satisfies very stringent separation axioms (T6) I was wondering if there was a weakening of these axioms such that the result still holds.