What are examples of Antiset? A set which transforms via converse functions is called antiset. Antisets usually arise in the context of Chu spaces.
I couldn't understand the notion of antiset and its examples.
 A: The definition of "antiset" given on the Wolfram MathWorld page you linked to (and also on Wiktionary!) is:

A set which transforms via converse functions.

This "definition" seems meaningless to me without more context. What is a "converse function"? What does it mean for a set to "transform via converse functions"? Is transforming via converse functions a property that a set may or may not have?
Digging a bit deeper, it seems that Vaughan Pratt (who is a leading proponent of Chu spaces, see here) uses the word "antiset" to mean an object of the category $\mathsf{Set}^{\text{op}}$ (the opposite category of the category of sets). See the second full paragraph on p. 3 of his paper Chu Spaces: Automata with quantum aspects.
Since the categories $\mathsf{Set}$ and $\mathsf{Set}^{\text{op}}$ have exactly the same objects, an antiset is just a set! The distinction between sets and antisets comes down to the morphisms between them. A morphism of antisets $X\to Y$ is just an ordinary function $Y\to X$. Now it's somewhat more clear what is meant by "transforming via converse functions"...
The category $\mathsf{Set}^{\text{op}}$ is well-known to be equivalent to the category $\mathsf{CABA}$ of complete atomic Boolean algebras (the equivalence is given by mapping a set to its powerset algebra and mapping a complete atomic Boolean algebra to its set of atoms). So you can also think of an antiset as a complete atomic Boolean algebra $B$ and a morphism of antisets $B\to C$ as a complete Boolean algebra homomorphism $B\to C$.
