Topological space objects in a topos II: ɛ-Completeness and ɛ-cocompleteness

It is well known that topoi satisfy strong internal completeness and cocompleteness conditions: Lawvere [4] announced the existence of internal Kan extensions; proofs may be found in Kock and Wraith [3] and Diaconescu [2]. In this paper I give an explicit construction of the limit of an internal functor and lift the completeness and cocompleteness of ? to the category of topological space objects in ? defined by internalizing the definition in terms of open sets (as in [7] and [8]).