Lattice properties of \(T_1-L\) topologies (Q1925600)
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scientific article; zbMATH DE number 6116577
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lattice properties of \(T_1-L\) topologies |
scientific article; zbMATH DE number 6116577 |
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Lattice properties of \(T_1-L\) topologies (English)
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18 December 2012
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The \(T_1\) separation axiom for \(L\)-topologies is studied. Some basic results for the set of all \(T_1\)-\(L\) topologies are proved. It is shown that the lattice of all such topologies is complete, it is neither atomic, nor modular nor complemented. The final result claims that the lattice of all \(T_1\)-\(L\) topologies has dual atoms (coatoms) if and only if \(L\) has dual atoms.
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\(L\)-topology
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fuzzy topology
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separation axioms
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\(T_1\)-topology
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lattice of topologies
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