Fuzzy topology with respect to continuous lattices

β-compactness in L-fuzzy Topological Spaces

“…When x α ∈ M(L X ) we shall call x and α the support of x α (x = Suppx α ) and the height of x α (α = h(x α )), respectively. Warner [18] has proved that the set ω(δ) of continuous functions, from a topological space (X, δ) to L with its Scott topology, is an L-topology. This provides a "goodness of extension" criterion for L-topological property.…”

Galois connections between categories of -topological spaces

“…Clearly, (X) is a stratified L-topological space for each topological space X. We refer to [8,11,14,19] for the evolution and more about these two functors. When L = [0, 1], the pair of functors ( , ) are called the Lowen functors in the literature and simply denoted ( , ).…”

“…Write L : Top −→ L-Top for the functor which sends every topological space (X, T ) to (X, L (T )), where L (T ) is the collection of all the Scott continuous functions X −→ L; and write L : L-Top −→ Top for the functor sending every L-topological space (X, ) to (X, L ( )), where L ( ) is the coarsest topology on X making all ∈ Scott continuous X −→ L. Then ( L , L ) is a Galois connection between the category Top of topological spaces and the category L-Top of L-topological spaces. See [11,14,19] for the evolution of this pair of functors.…”

Basic structures of fuzzy topology

“…Yet another extension w m of the functor w was introduced by M.W. Warner [197]. Its definition uses the so-called Scott topology [50] on the lattice L. In the case where L is completely distributive, w w = ~.…”