Given a pretopological space $(X,\mbox{cl})$ where $\mbox{cl}$ is a pretopological closure operator. How does one find the topological reflection of $(X,\mbox{cl})$?

I know of a way namely by determining the neighbourhoods of $(X,\mbox{cl})$ and then defining the topology $$\mathcal{T} := \{A \subseteq X \mid \forall a \in A: A \mbox{ is a neighbourhood of } a\}$$ but I read a proof in which they stated that this can be done directly by "a standard transfinite process", so my question is: does anyone know what transfinite process they mean here and how general is this process?


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