Abstract
It is shown in this paper that if a concrete category A \mathfrak {A} admits embedding as a full finitely productive subcategory of a cartesian closed topological (CCT) category, then A \mathfrak {A} admits such embedding into a smallest CCT category, its CCT hull. This hull is characterized internally by means of density properties and externally by means of a universal property. The problem is posed of whether every topological category has a CCT hull.
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