 
Summary: A New Category?
Domains, Spaces and Equivalence Relations
Dana S. Scott
School of Computer Science
Carnegie Mellon University
dana.scott@cs.cmu.edu
Version 1: Draft of 31 December 1996
Version 2: Corrected on 19 April 1998
1 Introduction.
The familiar categories SET and TOP , consisting of sets and arbitrary
mappings and of topological spaces and continuous mappings, have many
well known closure properties. For example, they are both complete and
cocomplete, meaning that they have all (small) limits and colimits. They
are wellpowered and cowellpowered, meaning that collections of subobjects
and quotients of objects can be represented by sets. They are also nicely
related, since SET can be regarded as a full subcategory of TOP , and the for
getful functor that takes a topological space to its underlying set preserves
limits and colimits (but reflects neither).
The category SET is also a cartesian closed category, meaning that the
functionspace construct or the internal homfunctor is very well behaved, in
