Bentley, H. L.; Herrlich, Horst Doitchinov’s construct of supertopological spaces is topological. (English) Zbl 0940.54016 Serdica Math. J. 24, No. 1, 21-24 (1998). D. Doitchinov [Sov. Math., Dokl. 5, 595-598 (1964); translation from Dokl. Akad. Nauk SSSR 156, 21-24 (1964; Zbl 0137.42101)] introduced supertopological spaces in order to obtain a unified theory of topological spaces, uniform spaces and proximity spaces. In the paper under review the authors prove that the construct SuperTop of all supertopological spaces and their continuous maps is topological and they derive some corollaries from this result. It is also shown that SuperTop fails to be Cartesian closed. Reviewer: Roni N.Levy (Sofia) Cited in 1 Document MSC: 54B30 Categorical methods in general topology 54E05 Proximity structures and generalizations 18D30 Fibered categories 54A05 Topological spaces and generalizations (closure spaces, etc.) 54E15 Uniform structures and generalizations Keywords:supertopological space; topological construct Citations:Zbl 0137.42101 PDFBibTeX XMLCite \textit{H. L. Bentley} and \textit{H. Herrlich}, Serdica Math. J. 24, No. 1, 21--24 (1998; Zbl 0940.54016) Full Text: EuDML