Here, we define (semi)topological L-algebras and some related results are approved. Then deduce conditions that mention an L-algebra to be a semi-topological or topological check attributes of them. Chiefly, display in L, if (L, ↠, τ ) is {1} open set L bounded satisfies the double negation property, then (L,τ) L-algebra. Finally, construct discrete topology on quotient L-algebra, under suit- a...

following the idea of $l$-fuzzy neighborhood system as introduced byfu-gui shi, and its generalization to $(l,m)$-fuzzy neighborhood system, the relationship between  $(l,m)$-fuzzy topology and $(l,m)$-fuzzy neighborhood system will be further studied. as an application of the obtained results, we will describe the initial structures of $(l,m)$-fuzzy neighborhood subspaces and $(l,m)$-fuzzy top...

in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

in 1997, fang proposed the concept of boundedness of $l$-fuzzy setsin $l$-topological vector spaces. since then, this concept has beenwidely accepted and adopted in the literature. in this paper,several characterizations of bounded $l$-fuzzy sets in$l$-topological vector spaces are obtained and some properties ofbounded $l$-fuzzy sets are investigated.

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

in this paper, we study some properties of the near sr-compactnessin l-topological spaces, where l is a fuzzy lattice. the near sr-compactness isa kind of compactness between lowen’s fuzzy compactness and sr-compactness,and it preserves desirable properties of compactness in general topologicalspaces.