On categories of supertopological spaces. (English) Zbl 0651.54004

The authors introduce the category \(\mathcal{SNBD}\) of neighborhood spaces and investigate its relations to various full subcategories. In particular, they demonstrate that \(\mathcal{SNBD}\) is a topological category, which contains the categories \(\text{Pr}\, \mathcal{TOP}\) of pretopological spaces, D. Doitchinov’s category \(\mathcal {STOP}\) of supertopological spaces, and hence the categories \(\mathcal{T}op\) of topological spaces and \(\text{Pr}\, ox\) of proximity spaces as nicely embedded full topological subcategories.
Reviewer: H.Herrlich


54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
54A05 Topological spaces and generalizations (closure spaces, etc.)
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
54E05 Proximity structures and generalizations
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