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
MSC:
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 |