The definition of Differential Manifold or Smooth Manifold include $\text{Second countability}$ and $\text{Hausdorffness condition}$.
My question is why we include Second countability and Hausdorffness in the defintition of Differentiable manifold?
I got something from a online article that Second countability is used to exclude large space .
But I could not mean it.
Can someone explain why we take Second Countability and Hausdorffness condition ?