Closed structures on categories of topological spaces (Q1060452)

It is proved that any full epireflective subcategory of the category Top of topological spaces admits exactly one symmetric monoidal closed structure. In 1979, the author published this result in the case of Top itself [see Comment. Math. Univ. Carol. 20, 431-446 (1979; Zbl 0416.18014)] but following \textit{G. M. Kelly} and \textit{F. Rossi} [Bull. Aust. Math. Soc. 31, 41-59 (1985; Zbl 0548.18005)] the proof contains a gap. Independently of the paper under review, it was re-proved by \textit{M. C. Pedicchio} and \textit{S. Solimini} [On a ''good'' dense class of topological spaces, Quaderno n. 100, Univ. Trieste (1984)] and the author affirm that their method applies to a general epireflective subcategory, too.