Lattice-valued convergence spaces and regularity
Copyright policy )Lattice-valued convergence spaces and regularity
The author continues his previous studies on lattice-valued convergence spaces. The main purpose of this paper is to use some duality conditions in order to characterize regularity of such spaces with the lattice in the form of a complete Heyting algebra. Moreover some separation axioms are introduced and they are used to prove some theorems on the regularity preservation. Yet another result derived in the paper is given by an extension theorem for continuous mappings from a dense subspace to a regular space. The regularity axiom presented in the paper is also characterized in the restricted lattice context of complete Boolean algebras.
- SEALS Consortium South Africa
- Rhodes University South Africa
\(L\)-fuzzy convergence, regularity, Fuzzy topology, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), pretopological space, continuous extension, T2-axiom, 510, diagonal condition, Extensions of spaces (compactifications, supercompactifications, completions, etc.), Lower separation axioms (\(T_0\)--\(T_3\), etc.), dense subset, T1-axiom, \(L\)-topology, \(L\)-diagonal filter, Continuous maps, \(L\)-filter, \(L\)-convergence space, Extension of maps
\(L\)-fuzzy convergence, regularity, Fuzzy topology, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), pretopological space, continuous extension, T2-axiom, 510, diagonal condition, Extensions of spaces (compactifications, supercompactifications, completions, etc.), Lower separation axioms (\(T_0\)--\(T_3\), etc.), dense subset, T1-axiom, \(L\)-topology, \(L\)-diagonal filter, Continuous maps, \(L\)-filter, \(L\)-convergence space, Extension of maps
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