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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)
##### Keywords:
topological category; approach space
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