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Doitchinov’s construct of supertopological spaces is topological. (English) Zbl 0940.54016

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.

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

Citations:

Zbl 0137.42101
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