On Continuity of Symmetric Restrictions of Borel Functions
On Continuity of Symmetric Restrictions of Borel Functions
We prove that if $X$ is a complete metric space dense-in-itself, $Y$ is a compact metric space and $F:X \times X\backslash \left \{ {(x,x):x \in X} \right \} \to Y$ is a Borel-measurable function such that $F({x_1},{x_2}) = F({x_2},{x_1})$ for every ${x_1},{x_2} \in X,{x_1} \ne {x_2}$, then there is a …