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In the paper "The Algebra of Topology" (Annals of Mathematics, 45, 1944), McKinsey and Tarski proposed derivative algebras (p183) to define the derive set in topology as follows.

Suppose $K$ is a Boolean algebra, $D$ is an operator in $K$ and $x,y\in K$. A derivative algebra satisfies the following axioms:

  1. $D(x)$ is closed in $K$.
  2. $DD(x) \leq D(x)$
  3. $D(x+y)=D(x)+D(y)$
  4. $D(0)=0$

I wonder if this is the first time that the term derivative algebras appeared (formally) in literature.

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