Let $(X,\tau)$ be a Hausdorff space. Denote by $\tau_{seq}$ the topology on $X$ whose closed sets are the sequentially $\tau$-closed subsets of $X$. From my understanding, the space $(X,\tau_{seq})$ is a sequential space.
Is there a book/paper where I can read more about the topological properties of $\tau_{seq}$ or sequential spaces in general?
The nlab page for sequential spaces mentions about their categorical properties which I am not interested in. I would like to know properties like metrizability or if such spaces are completely regular/normal.
More specifically, I am interested in the space $(X,w_{seq})$, where $X$ is a Banach space and $w$ its weak topology (generated by bounded linear functionals). This case is related to the sequential lower semicontinuity of some integral functional in calculus of variation that I am studying. Any account that covers only this case would suffice for my purpose.
PS. This question is a follow-up question to another one I asked on Mathoverflow earlier here.
