In this paper, we study the concept of weak linear fuzzy topology on a topological vector space as generalization usual topology. We prove that consists all weakly lower semi-continuous sets given when K (R or C) endowed with its case is different from topology, show not equivalent sets.

in this paper, we dene and study two operators s and s with grill.characterization and basic properties of these operators are obtained. also,we generalize a grill topological spaces via topology  s induced from operatorss and s.

motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by s. vickers, providing an algebraic and a coalgebraic category of the new structures. as a result, the nature of the category   topsys   of s. vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...