Topological \(\operatorname{FL}_{\operatorname{ew}}\)-algebras. (English) Zbl 1468.06013
Summary: The main goal of this article is to introduce topological \(\operatorname{FL}_{\operatorname{ew}}\)-algebras and study their main properties. We also treat completions of \(\operatorname{FL}_{\operatorname{ew}}\)-algebras with respect to inductive family of filters. This work generalizes similar works on MV-algebras [C. S. Hoo, Topology Appl. 81, No. 2, 103–121 (1997; Zbl 0896.06010)] and on \(\operatorname{FL}_{\operatorname{ew}}\)-algebras equipped with uniform topologies [S. Ghorbani and A. Hasankhani, PU.M.A., Pure Math. Appl. 21, No. 1, 15–26 (2010; Zbl 1265.03079)].
MSC:
| 06B30 | Topological lattices |
| 03G25 | Other algebras related to logic |
| 06D20 | Heyting algebras (lattice-theoretic aspects) |
| 06D35 | MV-algebras |
Keywords:
complete MV-algebra; inductive family; Heyting algebra; topological \(\operatorname{FL}_{\operatorname{ew}}\)-algebra; profinite \(\operatorname{FL}_{\operatorname{ew}}\)-algebra; Stone \(\operatorname{FL}_{\operatorname{ew}}\)-algebraReferences:
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