Lately, I've been really interested in compactifications of topological spaces, so I've started reading research papers about it. In the literature, I've found a very interesting idea, which is to order the distinct compactifications of a given space $X$ using partial orders, and (eventually) get a lattice.
It works like this: given two compactifications $\alpha_1 X$ and $\alpha_2 X$ of a noncompact topological space $X$, we define a relation $\alpha_1 X \preceq \alpha_2 X$ iff there exists a surjective continuous function $f: \alpha_2 X \to \alpha_1 X$ that leaves $X$ pointwise fixed (i.e. $f(x) = x$ for every $x \in X$). It turns out that in certain spaces $X$ (for example, when $X$ is locally compact) the relation $\preceq$ induces a lattice of lattice of compactifications of $X$.
I traced back this idea following the references of the first papers I found talking about this, the references in the references, etc., and I eventually found some papers dating back to the 1960s - 1970s: "The lattice of compactifications of a locally compact space" (Magill Jr., 1966), "On Hausdorff compactifications" (Rayburn, 1973), "Lattices of compactifications of Tychonoff spaces" (Ünlü, 1977), etc. However, all of them assume this idea as a well known thing.
I would like to know who came up with this idea, and what are the first papers/articles/books that talk about it (ideally I'd love to know the original one).