given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

In this paper we investigate generalized topologies generated by a subbase of preorder relators and consider its application in the concept of the complement. We introduce the notion of principal generalized topologies obtained from the new type of open sets and study some of their important properties.

Given a mapping $f:Xto X$ we naturally associate to it a monotonic map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, thus inducing a generalized topology on $X$. In this paper we investigate some properties of generalized topologies which are defined by such a procedure.

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

avila and molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). this work is a further investigation of generalized weak structures due to avila and molina. further we introduce the structures ro(g) and rc(g) and study the properties of the structur...

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...