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?

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- May 19th 2013, 04:28 PMblmalikovTopological 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?

- May 19th 2013, 04:47 PMblmalikovRe: 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.