Suppose $(Y,\tau')$ is Hausdorff and a function $f:(X,\tau)\to (Y,\tau')$ is a bijection such that $f^{-1}$ is continuous.
Can you show that $(X, \tau)$ is Hausdorff?
Suppose $(Y,\tau')$ is Hausdorff and a function $f:(X,\tau)\to (Y,\tau')$ is a bijection such that $f^{-1}$ is continuous.
Can you show that $(X, \tau)$ is Hausdorff?