Pretopological and topological lattice-valued convergence spaces. (English) Zbl 1115.54002
Author’s abstract: We show that the classical axiom which characterizes pretopological convergence spaces splits into two axioms in the general Heyting algebra-valued case. Furthermore, we present a generalization of Kowalski’s diagonal condition to the lattice-valued case.
Reviewer: Bernhard Behrens (Göteborg)
MSC:
| 54A40 | Fuzzy topology |
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 54G20 | Counterexamples in general topology |
Keywords:
\(L\)-fuzzy convergence; \(L\)-topology; \(L\)-filter; \(L\)-convergence space; limit space; pretopological space; diagonal condition; closure spaceReferences:
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