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Tower extension of topological constructs. (English) Zbl 1038.54006
Having a topological category \(\mathcal C\) and a completely distributive lattice \(L\), the author introduces the tower extension \(\mathcal C(L)\). It generalizes various constructions like approach spaces of R. Lowen or probabilistic convergence spaces of G. D. Richardson and D. C. Kent. Properties of tower extensions are studied.

MSC:
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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