$X$ is compact hausdroff topologic space.
$\tilde{X}=\{(x,y)\in X×X ; \hspace{2mm} x\neq y\}$.
Could you help me in proving that $C_0(\tilde{X})$ is a $\mathbb{T}$-separator?
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T- separating of continuouse function space that are zero in infinite on product topologic spacees
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