Scott convergence and fuzzy Scott topology on L-posets

Abstract

Abstract:We firstly generalize the fuzzy way-below relation on an L-poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified L-generalized convergence structure on an L-poset. In terms of that, L-fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified L-filters on an L-poset, and show that an L-poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.

The quasi Scott (Lawson) topology and q-continuous (q-algebraic) complete lattices

“…Many researchers are interested in continuous (algebraic) lattices, Scott (Lawson) topology, and their applications (see, for example, [1,4,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). In section 2 we define and study the quasi Scott topology on a complete lattice.…”