I define space as an element of an ordered semigroup action, that is a semigroup action conforming to a partial order. Topological spaces, uniform spaces, proximity spaces, directed graphs, metric spaces, etc. all are spaces. It can be further generalized to ordered precategory actions (that I call interspaces). I build basic general topology (continuity, limit, openness, closedness, hausdorffness, compactness, connectedness, etc.) in an arbitrary space. Now general topology is an algebraic theory.
For example, my generalized continuous function are: continuous function for topological spaces, proximally continuous functions for proximity spaces, uniformly continuous functions for uniform spaces, contractions for metric spaces, discretely continuous functions for (directed) graphs.
Was a spell laid onto Earth mathematicians not to find the most important structure in general topology until 2019?