Sequential convergence via Galois correspondences

Topological sequential spaces are the fixed points of a Galois correspondence between collections of open sets and sequential convergence structures. The same procedure can be followed replacing open sets by other topological concepts, such as closure operators or (ultra)filter convergences. The fixed points of these other Galois correspondences are not topological spaces in general, but they can be embedded into the larger topological classes of pretopological, pseudotopological and convergence spaces. In this paper, we characterize the sequential convergences which are fixed points of these correspondences as well as their restrictions to topological spaces.