Cartesian closed topological hulls

Herrlich, H.; Nel, L. D.

doi:10.1090/S0002-9939-1977-0476831-6

Cartesian closed topological hulls
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by H. Herrlich and L. D. Nel PDF

Proc. Amer. Math. Soc. 62 (1977), 215-222 Request permission

Abstract:

It is shown in this paper that if a concrete category $\mathfrak {A}$ admits embedding as a full finitely productive subcategory of a cartesian closed topological (CCT) category, then $\mathfrak {A}$ 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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