What's the origin of the term "chaotic topology"? If $X$ is a set, some sources* refer to the topology $\{\emptyset,X \}$ as the chaotic topology. (I've also seen it called the trivial, codiscrete, and indiscrete topology.) What is the origin of and motivation for this term? 
The term discrete topology makes sense to me because the restriction of the Euclidean topology on $\mathbb R$ to a set of discrete points results in the discrete topology. But I can see no such explanation for the term chaotic topology.
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 A: I don't know if this is the original motivation: When $\leq$ is a partial order on a set $S$, it induces a topology called the order topology, which is the one generated by the open rays $\{ c \in S : c < a \}, \{ c \in S : c > a \}$.
The order topology is chaotic precisely if the order is trivial, i.e. if every element is comparable only with itself.
This may explain "chaotic", as the antonym of "ordered".
It seems that a similar point of view was already taken by Felix Hausdorff in Grundzüge der Mengenlehre (1922). He talks about ordered sets in chapters 4–6, and in chapter 7 introduces a notion of a topological space. The introduction to chapter 7 (pp. 209–211) views an order as an example to give additional structure to a set, and goes on to explore generalizations of the concept of an order, and arrives at the notion of neighborhood. Hausdorff remarks that an order can be defined from a suitable system of neighborhoods:

Hier wird also eine Menge $M$ unter dem Gesichtspunkt einer Zuordnung zwischen Elementen und Teilmengen betrachtet; wir haben übrigens gezeigt (Kap. IV, § 1), daß man auch die Ordnung einer Menge durch ein passendes System von Teilmengen definieren kann.

I do not know who first used the word chaotic (or French chaotique, German chaotisch) in the context of topology. It does not appear in Hausdorff's book.
