# Weak Topology determined by identity maps [duplicate]

Let $(X,τ_1)$ and $(X,τ_2)$ be two tychonoff spaces. Let $τ$ be the smallest topology on X such that identity maps $id_1:(X,τ)→(X,τ_1)$ and $id_2:(X,τ)→(X,τ_2)$ are continuous. If both $(X,τ_1)$ and $(X,τ_2)$ are separable topological spaces. Then (X,τ) will be separable?