On Function Spaces. III

For topological \(T_{0}\) -spaces \(\mathbb{X}\) and \(\mathbb{Y}\) , we prove that the space \(\mathbb{Y}\) is H-sober if and only if the function space \(\mathbb{C}_{\mathcal{T}}(\mathbb{X},\mathbb{Y})\) endowed with a certain topology \(\mathcal{T}\) is H-sober.