historical order versus pedagogical order

Historical order is not necessarily pedagogical order. For example, the only reason integration preceded differentiation is because the notation needed for differentiation was lacking. Another example is General Topology. Historically, metric spaces were the first topological spaces considered, but the student is best served by a cold-turkey presentation of the general topological space, leaving metric spaces as a footnote for the students to explore on their own. Indeed, some simple things discovered very late, such as the 6-People Theorem and Kaprekar’s constant, should be presented in elementary school.
keywords: Mathematics, Calculus

arbitrary bouba, arbitrary kiki, rich structure: choose two

Case 1. arbitrary bouba, rich structure, restricted kiki: open entities.
Case 2. arbitrary kiki, rich structure, restricted bouba: closed entities.
Case 3. arbitrary bouba, arbitrary kiki, poor structure: extreme granularity (either extremely coarse-grained, or extremely fine-grained).
one possible interpretation: bouba = unions; kiki = intersections; structure = topology, with the archetypal example of an extremely coarse-grained topology being, of course, the indiscrete topology, and with the archetypal example of an extremely fine-grained topology being, of course, the discrete topology.
keywords: choices, General Topology, Point-Set Topology