Cartesian Closed Categories of Effective Domains
Perhaps the most important and striking fact of domain theory is that important categories of domains are cartesian closed. This means that the category has a terminal object, finite products, and exponents. The only problematic part for domains is the exponent, which in this setting means the space of continuous functions. Cartesian closed categories of domains are well understood and the understanding is in some sense essentially complete by the work of Jung , Smyth , and others.
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