Conclusion

Although more than a century old, pre-topology is largely unknown, even though its fields of application are extremely numerous and varied, in the formal, natural and human sciences, as well as in engineering.

Among practical methods for constructing pre-topological spaces, the use of binary relations is particularly interesting, as it is both natural in many cases (it is very often easy to check the occurrence or non-occurrence of the properties of reflexivity, symmetry and transitivity), simple (especially for non-mathematicians or non-engineers) and fruitful (e.g. in the social sciences, psychology, economics, geography). Other methods are more sophisticated (using Galois correspondences), more "ensemblist" (using collections of subsets) or more classical (using distance functions).

This article is an overview of pretopology. The author...